TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60002 ms.

The following DP Processors were used


Problem 1 was processed with processor PolynomialLinearRange4iUR (912ms).
 | – Problem 2 was processed with processor PolynomialLinearRange4iUR (754ms).
 |    | – Problem 3 was processed with processor DependencyGraph (6ms).
 |    |    | – Problem 4 was processed with processor ForwardNarrowing (5ms).
 |    |    |    | – Problem 5 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    | – Problem 6 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    | – Problem 7 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (16ms).
 |    |    |    |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (47ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (16ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (18ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (17ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (53ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (22ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (59ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (19ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (68ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (20ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (24ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (79ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (24ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (119ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (224ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (517ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 remains open; application of the following processors failed [ForwardNarrowing (358ms), ForwardNarrowing (460ms), ForwardNarrowing (370ms), ForwardNarrowing (635ms), ForwardNarrowing (485ms), ForwardNarrowing (424ms), ForwardNarrowing (507ms), ForwardNarrowing (753ms), ForwardNarrowing (577ms), ForwardNarrowing (728ms), ForwardNarrowing (568ms), ForwardNarrowing (749ms), ForwardNarrowing (566ms), ForwardNarrowing (752ms), ForwardNarrowing (576ms), ForwardNarrowing (754ms), ForwardNarrowing (563ms), ForwardNarrowing (640ms), ForwardNarrowing (159ms), ForwardNarrowing (580ms), ForwardNarrowing (589ms), ForwardNarrowing (485ms), ForwardNarrowing (147ms), ForwardNarrowing (581ms), ForwardNarrowing (614ms), ForwardNarrowing (791ms), ForwardNarrowing (629ms), ForwardNarrowing (596ms), ForwardNarrowing (579ms), ForwardNarrowing (715ms), ForwardNarrowing (775ms), ForwardNarrowing (300ms), ForwardNarrowing (690ms), ForwardNarrowing (445ms), ForwardNarrowing (1144ms), ForwardNarrowing (timeout)].

The following open problems remain:

Open Dependency Pair Problem 4

Dependency Pairs

mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(X1, X2, X3)) → mark#(X1)
a__if#(true, X, Y) → mark#(X)mark#(if(X1, X2, X3)) → a__if#(mark(X1), mark(X2), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, false, true, mark, a__f

Problem 1: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

mark#(if(X1, X2, X3)) → mark#(X2)a__if#(false, X, Y) → mark#(Y)
a__f#(X) → mark#(X)mark#(f(X)) → a__f#(mark(X))
mark#(if(X1, X2, X3)) → mark#(X1)a__if#(true, X, Y) → mark#(X)
mark#(f(X)) → mark#(X)a__f#(X) → a__if#(mark(X), c, f(true))
mark#(if(X1, X2, X3)) → a__if#(mark(X1), mark(X2), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

Polynomial Interpretation

Improved Usable rules

mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(f(X)) → a__f(mark(X))
a__if(true, X, Y) → mark(X)a__if(false, X, Y) → mark(Y)
a__f(X) → f(X)mark(false) → false
a__f(X) → a__if(mark(X), c, f(true))a__if(X1, X2, X3) → if(X1, X2, X3)
mark(true) → truemark(c) → c

The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:

a__if#(false, X, Y) → mark#(Y)

Problem 2: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

mark#(if(X1, X2, X3)) → mark#(X2)a__f#(X) → mark#(X)
mark#(if(X1, X2, X3)) → mark#(X1)mark#(f(X)) → a__f#(mark(X))
a__if#(true, X, Y) → mark#(X)mark#(f(X)) → mark#(X)
a__f#(X) → a__if#(mark(X), c, f(true))mark#(if(X1, X2, X3)) → a__if#(mark(X1), mark(X2), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, false, true, mark, a__f

Strategy

Polynomial Interpretation

Improved Usable rules

mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(f(X)) → a__f(mark(X))
a__if(true, X, Y) → mark(X)a__if(false, X, Y) → mark(Y)
a__f(X) → f(X)mark(false) → false
a__f(X) → a__if(mark(X), c, f(true))a__if(X1, X2, X3) → if(X1, X2, X3)
mark(true) → truemark(c) → c

The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:

a__f#(X) → mark#(X)mark#(f(X)) → mark#(X)
a__f#(X) → a__if#(mark(X), c, f(true))

Problem 3: DependencyGraph

Dependency Pair Problem

Dependency Pairs

mark#(if(X1, X2, X3)) → mark#(X2)mark#(f(X)) → a__f#(mark(X))
mark#(if(X1, X2, X3)) → mark#(X1)a__if#(true, X, Y) → mark#(X)
mark#(if(X1, X2, X3)) → a__if#(mark(X1), mark(X2), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The following SCCs where found

mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(X1, X2, X3)) → mark#(X1)
a__if#(true, X, Y) → mark#(X)mark#(if(X1, X2, X3)) → a__if#(mark(X1), mark(X2), X3)

Problem 4: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(X1, X2, X3)) → mark#(X1)
a__if#(true, X, Y) → mark#(X)mark#(if(X1, X2, X3)) → a__if#(mark(X1), mark(X2), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(X1, X2, X3)) → a__if#(mark(X1), mark(X2), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(mark(X1), true, X3) 
a__if#(mark(X1), a__f(mark(_x31)), X3) 
a__if#(a__f(mark(_x21)), mark(X2), X3) 
a__if#(false, mark(X2), X3) 
a__if#(mark(X1), false, X3) 
a__if#(c, mark(X2), X3) 
a__if#(true, mark(X2), X3) 
a__if#(mark(X1), c, X3) 
a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3) 
a__if#(mark(X1), a__if(mark(_x31), mark(_x32), _x33), X3) 
Thus, the rule mark#(if(X1, X2, X3)) → a__if#(mark(X1), mark(X2), X3) is replaced by the following rules:
mark#(if(X1, if(_x31, _x32, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)

Problem 5: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(X1, if(_x31, _x32, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)
a__if#(true, X, Y) → mark#(X)mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)
mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(X1, X2, X3)) → mark#(X1)
mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)
mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, false, true, mark, a__f

Strategy

The right-hand side of the rule mark#(if(X1, if(_x31, _x32, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), mark(_x32), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3) 
a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3) 
a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3) 
a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3) 
a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3) 
a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3) 
a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3) 
a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3) 
Thus, the rule mark#(if(X1, if(_x31, _x32, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), mark(_x32), _x33), X3) is replaced by the following rules:
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)

Problem 6: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X2)
mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
a__if#(true, X, Y) → mark#(X)mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)
mark#(if(X1, X2, X3)) → mark#(X1)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3) 
a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3) 
a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3) 
a__if#(mark(X1), if(a__f(mark(_x51)), mark(_x32), _x43), X3) 
a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3) 
a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3) 
a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3) 
a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3) 
Thus, the rule mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3) is replaced by the following rules:
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)

Problem 7: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X2)
mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)
mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)
mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)a__if#(true, X, Y) → mark#(X)
mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)
mark#(if(X1, X2, X3)) → mark#(X1)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)
mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, false, true, mark, a__f

Strategy

The right-hand side of the rule mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3) 
a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3) 
Thus, the rule mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3) is replaced by the following rules:
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)

Problem 8: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)
mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)
mark#(if(X1, X2, X3)) → mark#(X1)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
a__if#(true, X, Y) → mark#(X)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), mark(_x32), _x43), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3) 
a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3) 
a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3) 
a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3) 
a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3) 
a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3) 
a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3) 
a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3) 
Thus, the rule mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), mark(_x32), _x43), X3) is replaced by the following rules:
mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)
mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)

Problem 9: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)
mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(X1, X2, X3)) → mark#(X1)
mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)
mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)
mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X2)
mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
a__if#(true, X, Y) → mark#(X)mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, false, true, mark, a__f

Strategy

The right-hand side of the rule mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3) 
a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3) 
a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) 
Thus, the rule mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) is replaced by the following rules:
mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)

Problem 10: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)
mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)
mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(X1, X2, X3)) → mark#(X1)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)
mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)
mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X2)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)a__if#(true, X, Y) → mark#(X)
mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3) 
a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3) 
a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) 
Thus, the rule mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3) is replaced by the following rules:
mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Problem 11: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)
mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X1)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X2)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)a__if#(true, X, Y) → mark#(X)
mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, false, true, mark, a__f

Strategy

The right-hand side of the rule mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3) 
a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3) 
a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3) 
a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
Thus, the rule mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) is replaced by the following rules:
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)

Problem 12: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)
mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X1)
mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)
mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
a__if#(true, X, Y) → mark#(X)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3) 
a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
Thus, the rule mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) is replaced by the following rules:
mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)

Problem 13: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X1)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)
mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
a__if#(true, X, Y) → mark#(X)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)
mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, false, true, mark, a__f

Strategy

The right-hand side of the rule mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3) 
a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3) 
a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3) 
a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
Thus, the rule mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) is replaced by the following rules:
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, X2, X3)) → mark#(X1)mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X2)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)
mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)
mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
a__if#(true, X, Y) → mark#(X)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)
mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)
mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3) 
a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
Thus, the rule mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) is replaced by the following rules:
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)
mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, X2, X3)) → mark#(X1)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)
mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)
mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)a__if#(true, X, Y) → mark#(X)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, false, true, mark, a__f

Strategy

The right-hand side of the rule mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3) 
a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3) 
a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3) 
a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3) 
Thus, the rule mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) is replaced by the following rules:
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X1)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)
mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X2)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)a__if#(true, X, Y) → mark#(X)
mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)
mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) 
Thus, the rule mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) is replaced by the following rules:
mark#(if(f(f(f(_x51))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(true)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(X1, X2, X3)) → mark#(X1)
mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(true)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
a__if#(true, X, Y) → mark#(X)mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, false, true, mark, a__f

Strategy

The right-hand side of the rule mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__if(mark(f(mark(_x41))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(c)), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), false, _x43), X3) 
a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(mark(_x41))), if(if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
Thus, the rule mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3) is replaced by the following rules:
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(c)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(mark(_x41))), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), false, _x43), X3)

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X1)
mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)
mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(mark(_x41))), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(true)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X2)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)a__if#(true, X, Y) → mark#(X)
mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(c)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3) 
a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3) 
a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
Thus, the rule mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) is replaced by the following rules:
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3)mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, X2, X3)) → mark#(X1)mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(mark(_x41))), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(true)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)a__if#(true, X, Y) → mark#(X)
mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(c)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3)mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, false, true, mark, a__f

Strategy

The right-hand side of the rule mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(a__f(f(a__if(mark(_x51), true, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__if(mark(f(a__if(mark(_x51), mark(_x52), _x53))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(a__if(false, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(a__if(mark(_x51), c, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(a__if(mark(_x51), a__f(mark(_x61)), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(a__if(true, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(if(mark(_x51), mark(_x52), _x43))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(a__if(c, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(a__if(a__f(mark(_x61)), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3) 
a__if#(f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
a__if#(a__f(f(a__if(mark(_x51), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) 
Thus, the rule mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3) is replaced by the following rules:
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), true, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__f(mark(_x61)), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), c, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), mark(_x52), _x43))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), mark(_x52), _x53))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(if(mark(c), c, f(true)), false, _x43), X3)

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)
mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, X2, X3)) → mark#(X1)mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), mark(_x52), _x43))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), c, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(mark(_x41))), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), true, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(true)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), mark(_x52), _x53))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)a__if#(true, X, Y) → mark#(X)
mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(c)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)
mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__f(mark(_x61)), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3)mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__if(mark(false), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3) 
a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3) 
a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(a__f(a__f(false)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3) 
Thus, the rule mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3) is replaced by the following rules:
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(false)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)
mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(X1, X2, X3)) → mark#(X1)
mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), mark(_x52), _x43))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), c, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(mark(_x41))), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), true, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(false)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(true)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), mark(_x52), _x53))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, X2, X3)) → mark#(X2)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
a__if#(true, X, Y) → mark#(X)mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(c)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__f(mark(_x61)), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3)mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, false, true, mark, a__f

Strategy

The right-hand side of the rule mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3) 
a__if#(a__f(a__f(false)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3) 
a__if#(f(a__f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__if(mark(false), c, f(true))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), true, _x33), X3) 
a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), false, _x33), X3) 
a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3) 
Thus, the rule mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3) is replaced by the following rules:
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, X2, X3)) → mark#(X1)mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), mark(_x52), _x43))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), c, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(mark(_x41))), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), true, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(false)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(true)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), mark(_x52), _x53))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)a__if#(true, X, Y) → mark#(X)
mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(c)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)
mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__f(mark(_x61)), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3)mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x71)), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(a__f(mark(_x101)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x43), X3) 
a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x111)), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(a__f(mark(_x21)), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), a__if(mark(_x111), mark(_x112), _x113), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(a__if(mark(_x101), mark(_x102), _x103), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x43), X3) 
a__if#(true, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(c, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x43), X3) 
a__if#(mark(X1), if(a__if(mark(if(mark(_x81), mark(_x82), _x93)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(false, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) 
Thus, the rule mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3) is replaced by the following rules:
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x71), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x71)), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, if(_x111, _x112, _x113), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), a__if(mark(_x111), mark(_x112), _x113), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x93)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(if(mark(_x81), mark(_x82), _x93)), c, f(true)), mark(_x32), _x43), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(false, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x71, _x72, _x73), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x43), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(if(_x101, _x102, _x103), _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__if(mark(_x101), mark(_x102), _x103), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x43), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(true, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, f(_x111), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x111)), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(f(_x101), _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__f(mark(_x101)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__f(mark(_x31)), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(false, X2, X3)) → a__if#(false, mark(X2), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x71), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x71)), _x43), X3)mark#(if(X1, if(_x31, c, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), c, _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(true), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, X2, X3)) → mark#(X1)mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), mark(_x52), _x43))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(false, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x71, _x72, _x73), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), c, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(mark(_x41))), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), true, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(false)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(true)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(if(_x101, _x102, _x103), _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__if(mark(_x101), mark(_x102), _x103), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x93)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(if(mark(_x81), mark(_x82), _x93)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), mark(_x52), _x53))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x43), X3)
mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(X1, if(f(if(f(_x101), _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__f(mark(_x101)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)a__if#(true, X, Y) → mark#(X)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(c)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x43), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(true, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__f(mark(_x61)), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, if(_x111, _x112, _x113), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), a__if(mark(_x111), mark(_x112), _x113), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, f(_x111), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x111)), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3)
mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, false, true, mark, a__f

Strategy

The right-hand side of the rule mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(a__f(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__if(mark(f(a__f(mark(_x51)))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(a__f(false))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), c, _x33), X3) 
a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), c, _x43), X3) 
a__if#(a__f(f(f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(a__if(mark(mark(_x51)), c, f(true)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(a__f(c))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(a__f(mark(_x51)))), a__if(if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(a__f(a__f(mark(_x61))))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
a__if#(a__f(f(a__f(true))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) 
Thus, the rule mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3) is replaced by the following rules:
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(a__f(mark(_x51)))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(f(mark(c)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(f(f(_x61)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__f(mark(_x61))))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(f(false))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(false))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(f(c))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(c))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(mark(_x51)), c, f(true)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), c, _x43), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(true))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)
mark#(if(c, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), false, _x43))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(_x31, true, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__f(mark(_x51)))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(true), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(true), mark(_x32), _x43), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(a__f(mark(_x51)))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, f(f(_x51)), X3)) → a__if#(mark(X1), a__f(a__f(mark(_x51))), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), c, _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), true, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(f(false))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(false))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(mark(_x51)), c, f(true)))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), false, _x33), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(f(_x81), c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__f(mark(_x81)), c, _x73)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(if(_x81, _x82, _x83), _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(true, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), c, _x43), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), true, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), false, _x33), X3)mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(false)), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), f(false), X3)) → a__if#(a__f(mark(_x21)), a__f(false), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(false, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(mark(_x51)), c, f(true)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(c)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x71, _x72, _x73), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(true), c, f(true)))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__if(mark(mark(_x31)), c, f(true)), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), c, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), f(false), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__f(false), X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)
mark#(if(X1, if(f(if(false, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(false, mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(true, if(_x31, c, _x33), X3)) → a__if#(true, a__if(mark(_x31), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(f(true), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(f(f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, f(false), X3)) → a__if#(mark(X1), a__if(mark(false), c, f(true)), X3)
mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(f(_x21), if(f(true), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(true), mark(_x32), _x43), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(a__f(mark(_x51)))), c, f(true)), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(true, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(true, c, _x73)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(_x31, c, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), c, _x43), X3)
mark#(if(false, c, X3)) → a__if#(false, c, X3)mark#(if(f(f(if(c, c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(f(a__f(mark(_x41))), if(if(c, c, f(true)), c, _x43), X3)
mark#(if(f(f(false)), if(f(c), c, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), c, _x43), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(c, c, f(true)), c, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), false, _x53))), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(true))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(mark(_x61), mark(_x62), _x53), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(true)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(false, false, X3)) → a__if#(false, false, X3)
mark#(if(X1, if(f(if(true, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(true, mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(_x21), if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, f(if(_x51, _x52, _x53)), X3)) → a__if#(mark(X1), a__f(a__if(mark(_x51), mark(_x52), _x53)), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(f(f(f(true))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(a__f(true))), if(a__if(c, c, f(true)), c, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(false)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(if(true, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(true, c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), c, _x33), X3)mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(f(mark(_x51)))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(if(_x71, c, _x73)), _x32, _x43), X3)) → a__if#(false, if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(f(a__f(false)), if(if(mark(c), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x71, c, _x63)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(if(mark(_x71), c, _x63)), mark(_x32), _x33), X3)mark#(if(f(f(f(mark(c)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), true, _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), f(_x31), X3)) → a__if#(a__f(mark(_x21)), a__f(mark(_x31)), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(false))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(false))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X2)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x43), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(c, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__if(mark(f(false)), c, f(true)), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(true))), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(f(_x101), _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__f(mark(_x101)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x63)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(if(mark(_x71), mark(_x72), _x63)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(c)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), c, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), f(_x71), _x43), X3)) → a__if#(f(a__f(false)), if(if(mark(c), c, f(true)), a__f(mark(_x71)), _x43), X3)
mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(f(a__f(false)), if(if(c, c, f(true)), true, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x71, true, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), true, _x73)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(false, if(f(if(if(_x91, _x92, _x93), c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), false, _x43), X3)) → a__if#(mark(X1), if(a__f(true), false, _x43), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(f(a__if(mark(false), c, f(true))), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(false, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, false, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), false, _x73)), mark(_x32), _x33), X3)mark#(if(false, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(f(_x91), c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(a__if(mark(mark(_x41)), c, f(true))), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(false, if(c, c, _x33), X3)) → a__if#(false, a__if(c, c, _x33), X3)
mark#(if(false, if(f(if(_x71, c, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(if(mark(_x71), c, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(c, c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x43), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), false, _x33), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(true, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(f(c))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(c))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(f(f(a__f(true))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(false, if(f(true), _x32, _x43), X3)) → a__if#(false, if(a__f(true), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(f(f(false)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(c, c, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(c, c, _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x111, _x112, _x113), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), a__if(mark(_x111), mark(_x112), _x113), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(f(a__if(mark(false), c, f(true))), if(if(mark(c), c, f(true)), true, _x43), X3)mark#(if(X1, if(f(if(c, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(c, c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(c, c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(c, c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(c, c, _x33), X3)) → a__if#(true, a__if(c, c, _x33), X3)
mark#(if(X1, if(f(if(_x81, f(_x111), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x111)), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), a__f(mark(_x71)), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(true), true, _x43), X3)) → a__if#(mark(X1), if(a__f(true), true, _x43), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x43), X3)) → a__if#(f(a__f(false)), if(if(mark(c), c, f(true)), c, _x43), X3)mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x71), c, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(true)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(c, mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__if(mark(a__if(mark(false), c, f(true))), c, f(true)), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(_x31, c, _x33), X3)) → a__if#(false, a__if(mark(_x31), c, _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(true, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(true, a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)mark#(if(true, if(f(true), _x32, _x43), X3)) → a__if#(true, if(a__f(true), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x71), _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), a__f(mark(_x71)), _x43), X3)mark#(if(f(_x21), if(_x31, c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x71), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x71)), _x43), X3)
mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(false, mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(f(f(_x61)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__f(mark(_x61))))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(true, f(_x31), X3)) → a__if#(true, a__f(mark(_x31)), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X1)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), false, _x53))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(false, f(false), X3)) → a__if#(false, a__f(false), X3)mark#(if(if(_x21, _x22, _x23), f(_x31), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__f(mark(_x31)), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), true, _x33), X3)
mark#(if(f(f(f(c))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(c))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), mark(_x52), _x43))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), true, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), true, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(X1, f(c), X3)) → a__if#(mark(X1), a__f(c), X3)mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(true), f(_x71), _x43), X3)) → a__if#(mark(X1), if(a__f(true), a__f(mark(_x71)), _x43), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(false, if(f(if(_x71, c, _x73)), true, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), true, _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x71), _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), a__f(mark(_x71)), _x43), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(false, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(false)), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(c, f(false), X3)) → a__if#(c, a__f(false), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), true, _x33), X3)mark#(if(true, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(true, a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), c, _x43), X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(f(a__f(false)), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), false, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), mark(_x72), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(true, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(X1, if(f(if(false, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), c, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(true), if(_x71, _x72, _x73), _x43), X3)) → a__if#(mark(X1), if(a__f(true), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, true, X3)) → a__if#(false, true, X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), c, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), c, _x43), X3)
mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(false, if(f(if(c, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(true, c, _x33), X3)) → a__if#(mark(X1), a__if(true, c, _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), true, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), true, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(mark(_x41))), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), true, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(c, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(c, mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(false)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(f(true))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(c, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, c, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, f(false), X3)) → a__if#(mark(X1), f(false), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(true)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), c, _x43), X3)) → a__if#(mark(X1), if(a__f(true), c, _x43), X3)mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(f(_x81), _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__f(mark(_x81)), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(if(_x101, _x102, _x103), _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__if(mark(_x101), mark(_x102), _x103), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(mark(_x41))), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(a__f(true))), c, f(true)), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(false, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(false, c, _x73)), mark(_x32), _x33), X3)
mark#(if(false, if(f(if(f(_x91), c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(a__f(mark(_x91)), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), c, _x33), X3)
mark#(if(X1, if(f(if(if(_x81, _x82, _x83), c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x73)), mark(_x32), _x33), X3)mark#(if(f(f(f(f(_x61)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__f(mark(_x61))))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(c, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, false, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(false)), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), true, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(false, c, _x33), X3)) → a__if#(mark(X1), a__if(false, c, _x33), X3)
mark#(if(X1, f(true), X3)) → a__if#(mark(X1), a__f(true), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(true), _x32, _x43), X3)) → a__if#(c, if(a__f(true), mark(_x32), _x43), X3)mark#(if(false, if(f(if(_x71, c, _x73)), false, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x93)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(if(mark(_x81), mark(_x82), _x93)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), mark(_x52), _x53))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(true, mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(true), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)a__if#(true, X, Y) → mark#(X)
mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(true)), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, c, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(false, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(false, f(_x31), X3)) → a__if#(false, a__f(mark(_x31)), X3)mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(f(a__f(a__f(mark(_x51)))), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), true, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(f(f(false)), if(if(mark(c), c, f(true)), true, _x43), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(true, f(false), X3)) → a__if#(true, a__f(false), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(c, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(c, c, _x73)), mark(_x32), _x33), X3)
mark#(if(c, f(_x31), X3)) → a__if#(c, a__f(mark(_x31)), X3)mark#(if(X1, if(c, c, _x43), X3)) → a__if#(mark(X1), if(c, c, _x43), X3)
mark#(if(f(f(false)), if(f(c), f(_x71), _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), a__f(mark(_x71)), _x43), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(c)), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(c, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(f(f(f(c))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(c, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__if(mark(mark(_x41)), c, f(true))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(f(f(false)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(c, if(c, c, _x33), X3)) → a__if#(c, a__if(c, c, _x33), X3)
mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), false, _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__f(mark(_x61)), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), c, _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(if(false, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(false, c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(_x71), mark(_x72), _x73), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), f(mark(_x31)), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(c, if(_x31, c, _x33), X3)) → a__if#(c, a__if(mark(_x31), c, _x33), X3)mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x71, f(_x81), _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), a__f(mark(_x81)), _x73)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, if(_x81, _x82, _x83), _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), a__if(mark(_x81), mark(_x82), _x83), _x73)), mark(_x32), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), true, _x33), X3) 
a__if#(mark(X1), if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x43), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(a__f(mark(_x111))), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(false, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3) 
a__if#(c, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(if(c, a__f(mark(_x91)), _x73)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(false), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(true), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), c, _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__if(mark(mark(_x91)), c, f(true)), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(true, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), false, _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(a__if(mark(_x111), mark(_x112), _x113)), _x83)), c, f(true)), mark(_x32), _x33), X3) 
Thus, the rule mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3) is replaced by the following rules:
mark#(if(X1, if(f(if(c, f(f(_x111)), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(a__f(mark(_x111))), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, f(_x91), _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), true, _x33), X3)mark#(if(false, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, f(true), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(true), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__if(mark(mark(_x91)), c, f(true)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(c, a__f(mark(_x91)), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(c, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(c, f(false), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(false), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(true, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, f(if(_x111, _x112, _x113)), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(a__if(mark(_x111), mark(_x112), _x113)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), false, _x43))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), if(_x71, _x72, _x73), _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(f(c), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(c, if(f(if(c, _x82, _x83)), false, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), false, _x43), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(false), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(mark(_x51)), c, f(true)))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x73)), f(_x61), _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(f(_x81), c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__f(mark(_x81)), c, _x73)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(c, c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x43), X3)mark#(if(true, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), if(c, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(c, _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(c, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(f(f(false)), if(f(c), c, _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), c, _x43), X3)
mark#(if(f(_x21), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(true, if(f(true), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(false)), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x43), X3)) → a__if#(a__f(true), if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x43), X3)
mark#(if(if(c, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(c, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(true, c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(true, c, _x63), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(false, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(c), if(if(c, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(c, mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(mark(_x51)), c, f(true)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x71, _x72, _x73), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(c, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(true), c, f(true)))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(f(if(_x61, false, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), false, _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__if(mark(mark(_x31)), c, f(true)), X3)
mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x43), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x43), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), true, _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(if(_x111, _x112, _x113), _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(a__if(mark(_x111), mark(_x112), _x113), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(X1, if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), f(false), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__f(false), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(f(c)), if(f(c), true, _x43), X3)) → a__if#(a__f(a__f(c)), if(if(c, c, f(true)), true, _x43), X3)mark#(if(f(false), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(false), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(false), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(false), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, true, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(f(f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, f(false), X3)) → a__if#(mark(X1), a__if(mark(false), c, f(true)), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(true, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(true, false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, true, _x73), _x43), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x73)), false, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(a__f(mark(_x51)))), c, f(true)), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(true, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(true, c, _x73)), mark(_x32), _x33), X3)
mark#(if(false, c, X3)) → a__if#(false, c, X3)mark#(if(f(f(if(c, c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(f(a__f(mark(_x41))), if(if(c, c, f(true)), c, _x43), X3)
mark#(if(f(f(false)), if(f(c), c, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), c, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), false, _x53))), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(true)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(false, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x93), c, _x73), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), if(if(mark(_x81), mark(_x82), _x93), c, _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(mark(_x101), false, _x83), _x73), _x33), X3)
mark#(if(if(false, _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(false, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(false, false, X3)) → a__if#(false, false, X3)
mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(c, c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(c, c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(_x21), if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3)
mark#(if(f(f(false)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(if(_x91, _x92, _x93), false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__if(mark(_x91), mark(_x92), _x93), false, _x103), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(if(mark(_x71), mark(_x72), _x83)), mark(_x32), _x43), X3)
mark#(if(X1, f(if(_x51, _x52, _x53)), X3)) → a__if#(mark(X1), a__f(a__if(mark(_x51), mark(_x52), _x53)), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), f(true)), X3)) → a__if#(f(true), if(if(mark(c), c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), false, _x63), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, false, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), false, _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, c, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), c, _x83), c, _x63), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(f(f(f(true))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(a__f(true))), if(a__if(c, c, f(true)), c, _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x43), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), c, _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), f(_x71), _x43), X3)) → a__if#(a__f(a__f(c)), if(if(c, c, f(true)), a__f(mark(_x71)), _x43), X3)
mark#(if(f(true), if(f(c), if(if(false, true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(false, true, _x93), c, _x63), _x33), X3)mark#(if(f(f(f(if(f(_x71), _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(a__f(mark(_x71)), mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), a__if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(false, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x63)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(if(mark(_x71), c, _x63)), mark(_x32), _x33), X3)mark#(if(f(f(f(mark(c)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, c, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(c, c, _x63), _x33), X3)mark#(if(X1, if(f(if(false, _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(false, mark(_x72), _x73)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(f(true), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(f(_x81), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), true, _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(f(_x61))), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(a__f(mark(_x61)))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), true, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), true, _x43), X3)
mark#(if(if(true, _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, true, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), true, _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(true))), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__if(mark(f(false)), c, f(true)), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(false), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(false), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(if(_x21, if(_x51, _x52, _x53), _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, c, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), c, _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(f(_x101), _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__f(mark(_x101)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(true), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), if(a__if(mark(c), c, f(true)), c, _x43), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), if(c, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(c, true, _x63), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x63)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(if(mark(_x71), mark(_x72), _x63)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__if(mark(f(false)), c, f(true)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, true, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, c, _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(c), c, f(true))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), c, _x33), X3)
mark#(if(f(true), if(f(c), if(if(true, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(true, mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), false, _x63), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(f(a__f(false)), if(if(c, c, f(true)), true, _x43), X3)mark#(if(X1, if(f(if(_x71, true, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), true, _x73)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(true), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(true), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(f(false), false, _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(c, if(f(if(c, true, _x83)), false, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, true, _x83)), c, f(true)), false, _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, true, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), true, _x83), c, _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(true), false, _x43), X3)) → a__if#(mark(X1), if(a__f(true), false, _x43), X3)mark#(if(X1, if(f(c), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(c), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(c, if(_x31, true, _x33), X3)) → a__if#(c, a__if(mark(_x31), true, _x33), X3)
mark#(if(true, if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(true, if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(f(_x41), _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, true, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), true, _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x43), X3)) → a__if#(a__f(true), if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x43), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(f(_x91), c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(if(c, true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(c, true, _x93), c, _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(if(_x71, c, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(if(mark(_x71), c, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, c, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(c, c, f(true)), true, _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x43), X3)) → a__if#(a__f(a__f(c)), if(if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), false, _x33), X3)
mark#(if(f(f(f(c))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(c))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(true, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x91), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(mark(_x82)), c, _x63), _x33), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(f(f(a__f(true))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(c), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(if(false, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(false, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(f(if(false, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(false, mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(true, c, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, c, _x83), c, _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), c, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), c, _x43), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(a__f(false), mark(_x62), _x53), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, false, _x73), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(if(mark(c), c, f(true)), if(c, false, _x73), _x43), X3)
mark#(if(X1, if(f(if(c, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(c, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(c, mark(_x102), _x103), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x81, f(_x111), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x111)), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(c, if(f(if(c, if(_x91, _x92, _x93), _x83)), false, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), false, _x33), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, true, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), true, _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), true, _x43), X3)) → a__if#(mark(X1), if(a__f(true), true, _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x71), c, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), c, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(mark(c), c, f(true))), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(c, mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(c, if(f(if(c, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(true, if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(true, if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x51)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(if(_x21, c, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), c, _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(_x31, c, _x33), X3)) → a__if#(false, a__if(mark(_x31), c, _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x51)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(true), if(f(c), if(if(if(_x111, _x112, _x113), _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(a__if(mark(_x111), mark(_x112), _x113), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x71, true, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), true, _x73)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), mark(_x62), _x63), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x33), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(if(mark(_x21), mark(_x22), _x33), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(true, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(true, a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)
mark#(if(true, if(f(true), _x32, _x43), X3)) → a__if#(true, if(a__f(true), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(X1, if(f(c), if(c, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(a__f(a__f(c)), if(if(c, c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(if(f(_x41), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, false, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), false, _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, _x62, _x73), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x43), X3)mark#(if(c, if(f(if(c, _x82, _x73)), c, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, c, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), c, _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(c, c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, true, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), true, _x83), c, _x63), _x33), X3)mark#(if(f(if(true, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(true, mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(false, mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(f(f(_x61)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__f(mark(_x61))))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(true, f(_x31), X3)) → a__if#(true, a__f(mark(_x31)), X3)mark#(if(X1, X2, X3)) → mark#(X1)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(false, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, false, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(false, f(false), X3)) → a__if#(false, a__f(false), X3)
mark#(if(if(_x21, _x22, _x23), f(_x31), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__f(mark(_x31)), X3)mark#(if(f(true), if(f(c), if(if(if(_x111, _x112, _x113), true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(a__if(mark(_x111), mark(_x112), _x113), true, _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), f(false), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__f(false), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), true, _x33), X3)mark#(if(f(f(f(c))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(c))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), true, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(false), c, f(true)), false, _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(c, if(f(if(c, c, _x83)), false, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, c, _x83)), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(f(true), if(f(c), if(if(c, true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(mark(c), c, f(true)), a__if(if(c, true, _x93), c, _x63), _x43), X3)
mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), true, _x43), X3)mark#(if(if(false, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(false, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(c, if(f(if(c, f(_x111), _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, a__f(mark(_x111)), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(c), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(c), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(X1, f(c), X3)) → a__if#(mark(X1), a__f(c), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)
mark#(if(X1, if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(X1, if(f(true), f(_x71), _x43), X3)) → a__if#(mark(X1), if(a__f(true), a__f(mark(_x71)), _x43), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), true, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), true, _x33), X3)mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)
mark#(if(false, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(X1, if(f(c), if(c, c, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)mark#(if(f(false), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(_x61, false, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(c, f(false), X3)) → a__if#(c, a__f(false), X3)
mark#(if(f(f(c)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(c, c, f(true)), true, _x33), X3)mark#(if(f(_x21), if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(true, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(true, a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), c, _x43), X3)
mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(f(a__f(false)), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(c), if(_x61, c, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, c, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), c, _x83), c, _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(if(_x111, _x112, _x113), true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(a__if(mark(_x111), mark(_x112), _x113), true, _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(f(_x111)), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(a__f(mark(_x111))), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(false, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(false, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(f(c), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__if(mark(mark(_x91)), c, f(true)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, c, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), c, _x103), _x73), _x33), X3)mark#(if(X1, if(f(c), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, f(_x111), _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), a__f(mark(_x111)), _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(if(c, _x82, _x83)), _x32, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), c, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), c, _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(false, if(f(if(c, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(false), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(X1, if(f(if(_x71, false, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), false, _x73)), mark(_x32), _x43), X3)
mark#(if(f(f(c)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(true), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(a__f(mark(_x71)), mark(_x62), _x53), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), true, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), true, _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x93), c, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(if(mark(_x81), mark(_x82), _x93), c, _x73), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, if(_x121, _x122, _x123), _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), a__if(mark(_x121), mark(_x122), _x123), _x93), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), false, _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, _x62, _x73), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x43), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(c), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), true, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(_x51)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(c, c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(a__f(false), false, _x63), true, _x43))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(f(if(_x61, f(_x71), _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), a__f(mark(_x71)), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(f(true))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, f(_x101), _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(c, a__f(mark(_x101)), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(c), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, f(false), X3)) → a__if#(mark(X1), f(false), X3)mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(c, if(f(if(c, if(_x111, _x112, _x113), _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, a__if(mark(_x111), mark(_x112), _x113), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x83)), false, _x33), X3)) → a__if#(c, a__if(if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), false, _x33), X3)mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(f(_x81), _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__f(mark(_x81)), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(if(_x101, _x102, _x103), _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__if(mark(_x101), mark(_x102), _x103), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(c), c, f(true))), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(c, c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(if(_x21, c, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), c, _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(_x61, c, _x63), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x43), X3)mark#(if(X1, if(f(if(false, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(false, c, _x73)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(c, if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(false)), c, f(true)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(false, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, mark(_x102), _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), false, _x63), true, _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(_x51, c, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), c, _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(f(f(_x61)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__f(mark(_x61))))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(true), if(f(c), if(if(false, true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(false, true, _x93), c, _x63), _x33), X3)
mark#(if(f(_x21), if(_x31, true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), true, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), true, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)mark#(if(X1, f(true), X3)) → a__if#(mark(X1), a__f(true), X3)
mark#(if(c, if(f(true), _x32, _x43), X3)) → a__if#(c, if(a__f(true), mark(_x32), _x43), X3)mark#(if(false, if(f(if(_x71, c, _x73)), false, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x93)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(if(mark(_x81), mark(_x82), _x93)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(if(_x41, _x42, _x43)), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), false, _x63), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(_x51, if(_x61, _x62, _x63), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(true, mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, if(_x111, _x112, _x113), _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), a__if(mark(_x111), mark(_x112), _x113), _x83), c, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(a__f(false), false, _x53), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(c), if(f(_x81), c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), c, _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, false, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), false, _x83), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), mark(_x62), _x63), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(if(_x101, _x102, _x103), _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(a__if(mark(_x101), mark(_x102), _x103), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, _x102, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(mark(_x101), mark(_x102), _x83), _x73), _x33), X3)
a__if#(true, X, Y) → mark#(X)mark#(if(c, if(f(if(c, f(_x91), _x83)), false, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), false, _x33), X3)
mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(true)), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, c, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), c, _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(X1, if(f(c), if(false, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(false, c, _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(c, false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), if(a__if(mark(_x81), mark(_x82), _x83), c, _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, f(_x111), _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), a__f(mark(_x111)), _x83), c, _x63), _x33), X3)
mark#(if(false, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(f(_x101), _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(a__f(mark(_x101)), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(f(a__f(a__f(mark(_x51)))), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), true, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(f(f(false)), if(if(mark(c), c, f(true)), true, _x43), X3)mark#(if(f(true), if(f(c), if(if(f(_x111), true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(a__f(mark(_x111)), true, _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(f(_x101), c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__f(mark(_x101)), c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(c), if(_x61, c, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(mark(_x61), c, _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), c, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), c, _x43), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)
mark#(if(f(f(_x51)), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(true, f(false), X3)) → a__if#(true, a__f(false), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(f(if(_x61, _x62, _x53)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(if(mark(_x61), mark(_x62), _x53)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(true, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(f(f(false)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x71), _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), a__f(mark(_x71)), _x43), X3)mark#(if(X1, if(c, c, _x43), X3)) → a__if#(mark(X1), if(c, c, _x43), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(_x21), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(c, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, true, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), true, _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(c, if(f(if(c, true, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, true, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)
mark#(if(f(c), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), f(_x71), _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), a__f(mark(_x71)), _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, f(_x101), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__f(mark(_x101)), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x51)), if(f(c), if(c, true, _x73), _x43), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x43), X3)mark#(if(if(f(_x41), _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(true, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(true, mark(_x102), _x103), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, true, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(mark(_x51)), c, f(true))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(true), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__f(true), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(c, if(f(if(c, false, _x83)), false, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, false, _x83)), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x72), _x73)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), mark(_x62), _x63), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), false, _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(if(_x61, if(_x71, _x72, _x73), _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), a__if(mark(_x71), mark(_x72), _x73), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(c)), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), c, _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(f(_x91), _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), if(if(c, true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(c, true, _x93), c, _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x43), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(if(_x21, true, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), true, _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), f(mark(_x31)), X3)mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x73), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(true), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(f(false), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(false, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, f(_x121), _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), a__f(mark(_x121)), _x93), c, _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(c), c, f(true))), a__if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(f(f(f(if(if(_x71, _x72, _x73), _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(a__if(mark(_x71), mark(_x72), _x73), mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x71, if(_x81, _x82, _x83), _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), a__if(mark(_x81), mark(_x82), _x83), _x73)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(c)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, if(_x111, _x112, _x113), _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), a__if(mark(_x111), mark(_x112), _x113), _x103), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(c)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(c), if(c, _x62, _x73), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x43), X3)
mark#(if(f(true), if(f(c), if(if(f(_x71), true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(mark(c), c, f(true)), a__if(if(a__f(mark(_x71)), true, _x93), c, _x63), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), mark(_x62), _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), if(c, true, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(c, true, _x63), _x33), X3)
mark#(if(true, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(if(mark(c), c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, f(_x91), _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(c, a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(false), c, f(true)), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(f(f(c)), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(c, c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, if(_x51, _x52, _x53), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, true, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), true, _x103), _x73), _x33), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, f(_x101), _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, a__f(mark(_x101)), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, _x102, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(_x21), if(f(true), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, c, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), c, _x93), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(a__f(false), false, _x63), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__f(mark(_x51)))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(a__f(mark(_x71)), mark(_x62), _x63), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__if(mark(f(true)), c, f(true)), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(f(mark(_x71)), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, true, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(true), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(true), mark(_x32), _x43), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(a__f(mark(_x51)))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(f(false), false, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__f(mark(_x71)), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, f(f(_x51)), X3)) → a__if#(mark(X1), a__f(a__f(mark(_x51))), X3)mark#(if(X1, if(f(if(f(_x91), _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(a__f(mark(_x91)), mark(_x72), _x73)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), c, _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(if(_x21, c, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), c, _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), true, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(f(false))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(false))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), false, _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(if(_x81, _x82, _x83), _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x43), X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), true, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, if(_x111, _x112, _x113), _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), a__if(mark(_x111), mark(_x112), _x113), _x83), c, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), f(false), X3)) → a__if#(a__f(mark(_x21)), a__f(false), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(false, if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(a__f(false), false, _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(c)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), false, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), false, _x43), X3)
mark#(if(true, if(_x31, true, _x33), X3)) → a__if#(true, a__if(mark(_x31), true, _x33), X3)mark#(if(false, if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(false, if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, if(_x121, _x122, _x123), _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), a__if(mark(_x121), mark(_x122), _x123), _x93), c, _x63), _x33), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), c, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(f(_x81)), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__f(a__f(mark(_x81))), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, if(_x101, _x102, _x103), _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73)), mark(_x32), _x43), X3)mark#(if(f(f(c)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(X1, if(f(if(false, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(false, mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(c, c, f(true)), if(c, false, _x73), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(true, if(_x31, c, _x33), X3)) → a__if#(true, a__if(mark(_x31), c, _x33), X3)mark#(if(f(_x21), if(f(c), if(if(true, true, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, true, _x83), c, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(f(true), mark(_x32), _x43), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(if(c, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(c, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)mark#(if(f(f(true)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(true)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, false, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), false, _x83), c, _x63), _x33), X3)mark#(if(X1, if(f(if(false, c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(false, c, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), true, _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(if(_x101, _x102, _x103), _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(a__if(mark(_x101), mark(_x102), _x103), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(c), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(true), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(true), mark(_x32), _x43), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x73), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), if(if(mark(_x81), true, _x93), c, _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__f(f(c)), a__if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(f(false), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(false), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(c, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), true, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(if(c, true, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, true, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(_x31, c, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), c, _x43), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(c, c, f(true)), c, _x43), X3)
mark#(if(f(f(c)), if(f(c), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(true))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(mark(_x61), mark(_x62), _x53), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(c)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(false), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(false), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x33), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(if(mark(_x21), mark(_x22), _x33), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), c, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(f(_x111), _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(a__f(mark(_x111)), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(X1, if(f(if(true, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(true, mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x33), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(if(mark(_x21), mark(_x22), _x33), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(c, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(c, mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(X1, if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)
mark#(if(X1, if(f(if(c, _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(c, mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(f(if(_x51, true, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), true, _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(a__f(false), mark(_x62), _x63), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(c)), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(false)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, true, _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, c, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(a__f(false), mark(_x62), _x63), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(false, if(f(if(true, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(true, c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(f(false), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(f(mark(_x51)))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(false, if(f(if(_x71, c, _x73)), _x32, _x43), X3)) → a__if#(false, if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(f(a__f(false)), if(if(mark(c), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), false, _x33), X3)mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), true, _x43), X3)
mark#(if(X1, if(f(if(c, f(if(_x111, _x112, _x113)), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(a__if(mark(_x111), mark(_x112), _x113)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), f(_x31), X3)) → a__if#(a__f(mark(_x21)), a__f(mark(_x31)), X3)
mark#(if(f(_x21), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(f(true), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x83), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(mark(_x101), false, _x83), _x73), _x33), X3)mark#(if(c, if(f(if(c, _x82, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(if(mark(if(c, mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)
mark#(if(c, if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(c, if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(f(f(f(false))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(false))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(c), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(if(c, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(c, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x43), X3)
mark#(if(X1, X2, X3)) → mark#(X2)mark#(if(false, if(f(true), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(c, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)
mark#(if(if(_x21, false, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), false, _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(f(true), if(f(c), if(if(true, true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(mark(c), c, f(true)), a__if(if(true, true, _x93), c, _x63), _x43), X3)
mark#(if(f(if(_x51, _x52, _x43)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(if(mark(_x51), mark(_x52), _x43)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(c, c, f(true)), false, _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x43), X3)mark#(if(f(true), if(f(c), if(if(_x81, false, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), false, _x93), c, _x63), _x33), X3)
mark#(if(f(c), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(false), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(false), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x83), c, _x63), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x43), X3)mark#(if(f(true), if(f(c), if(if(false, true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(mark(c), c, f(true)), a__if(if(false, true, _x93), c, _x63), _x43), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(c)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(false), c, f(true)), false, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), c, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), c, _x43), X3)) → a__if#(a__f(a__f(c)), if(if(c, c, f(true)), c, _x43), X3)mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(false)), if(f(c), f(_x71), _x43), X3)) → a__if#(f(a__f(false)), if(if(mark(c), c, f(true)), a__f(mark(_x71)), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(true, if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x71, _x72, _x73), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)
mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), c, _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, if(_x51, _x52, _x53), _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(f(_x101), _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(a__f(mark(_x101)), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(true, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, if(f(if(if(_x91, _x92, _x93), c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(c), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), mark(_x62), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(if(f(_x111), _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(a__f(mark(_x111)), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x43), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), false, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(f(a__if(mark(false), c, f(true))), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x71, false, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), false, _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(f(if(c, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(c, mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(a__if(mark(mark(_x41)), c, f(true))), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(false, if(c, c, _x33), X3)) → a__if#(false, a__if(c, c, _x33), X3)mark#(if(c, if(f(true), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x43), X3)
mark#(if(X1, if(f(if(c, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, c, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), c, _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)
mark#(if(true, if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(a__f(false), false, _x63), true, _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(_x51)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(false, if(f(true), _x32, _x43), X3)) → a__if#(false, if(a__f(true), mark(_x32), _x43), X3)mark#(if(X1, if(f(true), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(c, c, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(c, c, _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x111, _x112, _x113), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), a__if(mark(_x111), mark(_x112), _x113), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, f(_x111), _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), a__f(mark(_x111)), _x83), c, _x63), _x33), X3)mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), if(if(f(_x111), true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(a__f(mark(_x111)), true, _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(c, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(f(a__if(mark(false), c, f(true))), if(if(mark(c), c, f(true)), true, _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(_x21), if(c, c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(c, c, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(c, c, f(true)), false, _x33), X3)
mark#(if(f(f(f(if(false, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(false, mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(true, if(c, c, _x33), X3)) → a__if#(true, a__if(c, c, _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x71), mark(_x72), _x73)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(c), if(c, f(_x101), _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(c, a__f(mark(_x101)), _x73), _x33), X3)
mark#(if(X1, if(f(if(true, c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(true, c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), a__f(mark(_x71)), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), c, _x43), X3)) → a__if#(f(a__f(false)), if(if(mark(c), c, f(true)), c, _x43), X3)
mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), mark(_x62), _x63), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(c, if(f(if(c, _x82, _x73)), true, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), true, _x33), X3)mark#(if(f(f(c)), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(true)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(c)), if(f(c), if(c, _x62, _x63), _x43), X3)) → a__if#(a__f(a__f(c)), if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x43), X3)mark#(if(if(_x21, false, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), false, _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x33), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(if(mark(_x21), mark(_x22), _x33), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__if(mark(a__if(mark(false), c, f(true))), c, f(true)), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)mark#(if(f(if(_x41, _x42, _x43)), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(if(c, _x82, _x83)), c, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(f(_x91), _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__f(mark(_x91)), mark(_x102), _x103), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(if(true, true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(true, true, _x93), c, _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(if(_x71, _x72, _x73), true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(mark(c), c, f(true)), a__if(if(a__if(mark(_x71), mark(_x72), _x73), true, _x93), c, _x63), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), true, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(if(false, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(false, mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(if(c, _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(c, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(true, mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x43), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(f(a__if(mark(_x61), mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(true, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(true, false, _x103), _x73), _x33), X3)
mark#(if(X1, if(false, true, _x33), X3)) → a__if#(mark(X1), a__if(false, true, _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(true, if(_x111, _x112, _x113), _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, a__if(mark(_x111), mark(_x112), _x113), _x83), c, _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__if(mark(c), c, f(true))), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x71), _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), a__f(mark(_x71)), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(a__f(false), false, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(_x31, c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), c, _x33), X3)mark#(if(X1, if(f(true), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x71), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x71)), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(if(_x21, if(_x51, _x52, _x53), _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(X1, if(f(if(c, f(false), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(false), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(true, f(_x111), _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, a__f(mark(_x111)), _x83), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(_x31, true, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), true, _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), false, _x53))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(if(c, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(true, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, c, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(mark(_x61), c, _x73), _x33), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(true, _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(true, mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), mark(_x52), _x43))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(true), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(false, if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(if(_x41, _x42, _x43)), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(if(_x91, _x92, _x93), false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__if(mark(_x91), mark(_x92), _x93), false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(true), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), true, _x33), X3)
mark#(if(f(f(false)), if(f(c), f(c), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__f(c), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x83)), true, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x71), _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), a__f(mark(_x71)), _x43), X3)mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x33), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(if(mark(_x21), mark(_x22), _x33), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(false)), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), f(_x71), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__f(mark(_x71)), _x43), X3)
mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x83), c, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(a__if(true, mark(_x82), _x83), c, _x73), _x33), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(c), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), if(c, false, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(c, false, _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), false, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(if(_x91, _x92, _x93), _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x102), _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), mark(_x72), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(f(f(if(true, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(true, mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(true, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(true)), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x43), X3)
mark#(if(f(f(c)), if(f(c), if(c, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(false, c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(false, c, _x63), _x33), X3)
mark#(if(if(_x21, true, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), true, _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(false, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(X1, if(f(true), if(_x71, _x72, _x73), _x43), X3)) → a__if#(mark(X1), if(a__f(true), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), c, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, true, X3)) → a__if#(false, true, X3)mark#(if(f(f(mark(c))), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x63)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(a__if(mark(c), mark(mark(_x82)), _x63), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)
mark#(if(X1, if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(a__if(mark(_x61), mark(_x62), _x63)), c, f(true)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(a__f(false), false, _x63), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(c), if(c, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(c, c, _x63), _x33), X3)
mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)mark#(if(f(_x21), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(if(c, false, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, false, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, f(_x121), _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), a__f(mark(_x121)), _x93), c, _x63), _x33), X3)
mark#(if(f(if(if(_x61, _x62, _x63), _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, c, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)
mark#(if(f(f(if(_x61, _x62, _x63))), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(a__if(mark(_x61), mark(_x62), _x63))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(true, c, _x33), X3)) → a__if#(mark(X1), a__if(true, c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x43), X3)mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(false, if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(_x31, true, _x33), X3)) → a__if#(false, a__if(mark(_x31), true, _x33), X3)mark#(if(f(f(f(if(_x61, c, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), c, _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(true), if(f(c), if(if(c, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(c, mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(c), if(c, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(c, a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(c)), if(f(c), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(a__f(false), false, _x53), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(c, if(f(if(c, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(c, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(c, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(mark(_x41))), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(true, if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(true), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(c, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(c, mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(false)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x53), _x43), X3)) → a__if#(f(true), if(a__if(mark(c), c, f(true)), if(if(mark(_x81), true, _x93), c, _x53), _x43), X3)
mark#(if(f(f(c)), if(f(c), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(c)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(if(mark(c), c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x33), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, c, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, false, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), false, _x93), c, _x63), _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(c), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(false, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(false, mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(c), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(if(c, c, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, c, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(c, c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(true)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(true), c, _x43), X3)) → a__if#(mark(X1), if(a__f(true), c, _x43), X3)
mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(c), if(c, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(c, false, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x71, f(_x101), _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), a__f(mark(_x101)), _x73)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(mark(_x41))), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, f(_x101), _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, a__f(mark(_x101)), _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(a__f(true))), c, f(true)), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(if(false, _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(false, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(if(f(_x91), c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(a__f(mark(_x91)), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(c, c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(f(_x41), _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(X1, if(f(if(if(_x81, _x82, _x83), c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x73)), mark(_x32), _x33), X3)
mark#(if(true, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(a__if(mark(_x81), mark(_x82), _x83), c, _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(c, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, false, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(false)), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(a__f(mark(_x81))), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(false, c, _x33), X3)) → a__if#(mark(X1), a__if(false, c, _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), false, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), mark(_x52), _x53))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(f(_x91), false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__f(mark(_x91)), false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(true), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(a__f(false), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(mark(_x71)), c, f(true)), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)
mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(c)), if(f(c), if(false, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)
mark#(if(X1, if(f(true), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(c, true, _x33), X3)) → a__if#(mark(X1), a__if(c, true, _x33), X3)
mark#(if(f(if(f(_x61), _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(true, true, _x33), X3)) → a__if#(mark(X1), a__if(true, true, _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(c, a__f(mark(_x91)), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(c, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(c, false, _x103), _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(f(f(true)), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(c, if(f(if(c, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(false, f(_x31), X3)) → a__if#(false, a__f(mark(_x31)), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(c), if(true, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(true, c, _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__if(mark(mark(_x61)), c, f(true)), _x33), X3)
mark#(if(X1, if(f(if(c, f(_x91), _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), true, _x33), X3)mark#(if(f(_x21), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(true, false, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, false, _x83), c, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(f(_x91), false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__f(mark(_x91)), false, _x103), _x73), _x33), X3)
mark#(if(X1, if(f(if(if(_x101, _x102, _x103), c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__if(mark(_x101), mark(_x102), _x103), c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), true, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), true, _x43), X3)mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x43), X3)) → a__if#(a__f(a__f(c)), if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)
mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)mark#(if(f(f(c)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x73), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), if(if(mark(_x81), true, _x93), c, _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), if(true, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(c, f(_x31), X3)) → a__if#(c, a__f(mark(_x31)), X3)mark#(if(X1, if(f(if(c, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(c, c, _x73)), mark(_x32), _x33), X3)
mark#(if(false, if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(false, if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), a__f(mark(_x71)), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(if(true, _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)
mark#(if(if(f(_x41), _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, c, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(c)), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(c), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x73)), _x32, _x43), X3)) → a__if#(c, if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), mark(_x32), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, f(_x91), _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), false, _x33), X3)mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(c, if(f(if(c, c, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(f(f(f(c))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(true), if(f(c), if(if(true, true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(true, true, _x93), c, _x63), _x33), X3)mark#(if(c, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__if(mark(mark(_x41)), c, f(true))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(f(f(false)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(_x51)), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), a__if(if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(true)), if(if(c, c, f(true)), false, _x43), X3)mark#(if(c, if(c, c, _x33), X3)) → a__if#(c, a__if(c, c, _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x61), _x43), X3)) → a__if#(a__f(f(false)), if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x43), X3)mark#(if(if(_x21, if(_x51, _x52, _x53), _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__f(mark(_x61)), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x41, _x42, _x43)), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(false, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(false, mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(f(if(_x51, false, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), false, _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(c), c, f(true))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(if(_x61, true, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), true, _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), f(if(_x81, _x82, _x83)), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x33), X3)
mark#(if(false, if(f(if(false, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(false, c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(c, if(f(if(c, false, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, false, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(_x71), mark(_x72), _x73), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x33), X3)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(false), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(false), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(f(false), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, false, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(true), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(c, if(_x31, c, _x33), X3)) → a__if#(c, a__if(mark(_x31), c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, c, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(c, c, _x63), _x33), X3)mark#(if(f(true), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(if(false, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(false, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x93)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(if(mark(_x81), c, _x93)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x71, f(_x81), _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), a__f(mark(_x81)), _x73)), mark(_x32), _x33), X3)mark#(if(if(_x21, false, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), false, _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(f(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x61, true, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), false, _x63), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(a__if(mark(a__if(mark(_x51), a__f(true), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x43), X3) 
a__if#(a__if(mark(a__if(false, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(mark(_x51), f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(mark(_x51), a__f(a__f(mark(_x81))), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(mark(_x51), a__if(mark(mark(_x61)), c, f(true)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(if(mark(_x51), a__f(mark(_x61)), _x43)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(c, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(mark(_x51), a__f(c), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(true, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) 
Thus, the rule mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3) is replaced by the following rules:
mark#(if(f(if(if(_x61, _x62, _x63), f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x43), X3)
mark#(if(f(if(mark(c), f(_x61), f(true))), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(_x51, f(_x61), _x43)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(if(mark(_x51), a__f(mark(_x61)), _x43)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(if(true, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(true, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(_x51, f(f(_x81)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__f(mark(_x81))), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(if(_x51, f(true), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(true), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__if(mark(mark(_x61)), c, f(true)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(if(false, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(false, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(if(c, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(_x51, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(if(_x51, f(c), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(c), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(if(f(_x61), f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)

Problem 26: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(if(true, if(_x31, _x32, _x33), X3)) → a__if#(true, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(if(if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x43), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(if(_x91, _x92, _x93), f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(true, if(f(true), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x43), X3)) → a__if#(a__f(true), if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x43), X3)
mark#(if(if(c, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(c, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, f(c), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(c), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(true, c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(true, c, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(c, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(c, mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(mark(_x51)), c, f(true)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(false), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(false), c, f(true)), if(a__if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(f(if(_x61, false, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), false, _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(if(true, true, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, true, _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(true, mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), a__if(mark(mark(_x31)), c, f(true)), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(if(_x91, _x92, _x93), f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), true, _x33), X3)mark#(if(if(if(_x41, if(_x71, _x72, _x73), _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), a__if(mark(_x71), mark(_x72), _x73), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), f(false), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__f(false), X3)mark#(if(X1, if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(if(c, f(if(_x81, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(a__if(mark(_x81), c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(mark(_x61)), c, f(true)), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), mark(_x72), _x73), _x63), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(false, mark(_x62), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(_x51), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(true, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(true, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, true, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(true), _x33), X3)
mark#(if(f(false), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(false), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, true, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, true, _x73), _x43), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x43), X3)mark#(if(if(f(_x41), f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(if(_x51, f(if(false, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(false, c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(c, false, _x83), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(c, false, _x83), _x73), _x33), X3)mark#(if(c, if(f(if(c, _x82, _x73)), false, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), false, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(true, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(true, c, _x73)), mark(_x32), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), mark(_x72), _x73), _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(if(c, c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(f(a__f(mark(_x41))), if(if(c, c, f(true)), c, _x43), X3)
mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(f(false)), if(f(c), c, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), c, _x43), X3)
mark#(if(f(c), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(c), c, f(true)), if(a__if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x43), X3)mark#(if(f(if(_x51, f(_x61), _x43)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(if(mark(_x51), a__f(mark(_x61)), _x43)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(if(if(true, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(true, mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(_x31, _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(f(_x91), false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(a__f(mark(_x91)), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(false, false, X3)) → a__if#(false, false, X3)
mark#(if(if(false, _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(false, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(if(c, c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(_x21), if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3)mark#(if(f(f(false)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(if(_x91, _x92, _x93), false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__if(mark(_x91), mark(_x92), _x93), false, _x103), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(if(mark(_x71), mark(_x72), _x83)), mark(_x32), _x43), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), f(true)), X3)) → a__if#(f(true), if(if(mark(c), c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x43), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(if(f(_x61), f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, false, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), false, _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(c), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(c), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, f(false), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(false), _x63), _x33), X3)
mark#(if(f(if(if(_x61, _x62, _x63), f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(true), if(f(c), if(if(false, true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(c, c, f(true)), a__if(if(false, true, _x93), c, _x63), _x43), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(if(if(_x41, f(_x71), _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), a__f(mark(_x71)), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), a__f(mark(_x71)), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(if(if(_x41, f(_x71), _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), a__f(mark(_x71)), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x43), X3)mark#(if(f(f(c)), if(f(c), f(_x71), _x43), X3)) → a__if#(a__f(a__f(c)), if(if(c, c, f(true)), a__f(mark(_x71)), _x43), X3)
mark#(if(if(_x21, f(true), _x23), if(f(c), if(mark(true), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(true), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(f(f(f(if(f(_x71), _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(a__f(mark(_x71)), mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x81), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(if(if(_x41, c, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), c, _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), f(_x51), _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(f(mark(c)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), if(mark(_x71), mark(_x72), _x83), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(_x21, f(mark(c)), _x23), if(f(c), if(mark(mark(c)), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(if(mark(_x81), a__f(mark(_x91)), _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(f(_x61), _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(a__f(mark(_x61)), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(if(false, _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(false, mark(_x72), _x73)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(if(c, f(_x61), f(true))), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(mark(_x61)), _x53)), c, f(true)), a__if(if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(true, if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(if(_x111, _x112, _x113)), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(a__if(mark(_x111), mark(_x112), _x113)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(if(true, f(_x51), _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(true, a__f(mark(_x51)), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(if(_x51, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(if(mark(_x61), mark(_x62), _x53), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(false, if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(c), if(c, _x62, _x73), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(if(true, if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__if(mark(f(false)), c, f(true)), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(f(true), if(f(c), if(if(_x81, c, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), c, _x93), c, _x63), _x33), X3)
mark#(if(f(if(_x51, f(if(false, false, _x83)), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(if(true, false, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(true, false, _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(_x61, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), if(a__if(mark(c), c, f(true)), c, _x43), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), f(c), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(c), c, f(true)), _x33), X3)
mark#(if(X1, if(f(c), if(c, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(c, true, _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__if(mark(f(false)), c, f(true)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, true, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x33), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(if(mark(_x21), a__f(mark(_x51)), _x33), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, c, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(c), c, f(true))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(if(true, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(true, mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), false, _x63), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, true, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), true, _x73)), mark(_x32), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, f(_x91)), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__f(mark(_x91)), _x73), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(c), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(c), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, c, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(c, if(f(if(c, true, _x83)), false, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, true, _x83)), c, f(true)), false, _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(c, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(c, false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, true, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), true, _x83), c, _x63), _x33), X3)
mark#(if(X1, if(f(true), false, _x43), X3)) → a__if#(mark(X1), if(a__f(true), false, _x43), X3)mark#(if(if(true, if(_x51, false, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), false, _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(true, _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(true, mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, f(_x91)), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(mark(_x61)), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__f(mark(_x91)), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), true, _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)mark#(if(f(if(_x51, f(if(true, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(true, mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(false, if(f(if(_x71, c, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(if(mark(_x71), c, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, c, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), c, _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(if(true, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(true, f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(c, c, f(true)), true, _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(a__f(mark(_x51))), c, f(true)), if(a__if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x43), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(a__f(mark(_x81))), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), false, _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(true, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(false, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(false, mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x83)), false, f(true)), X3)) → a__if#(c, if(if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), false, _x43), X3)mark#(if(if(true, _x22, _x23), if(f(c), if(c, f(_x101), _x73), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, a__f(mark(_x101)), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(true, c, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, c, _x83), c, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), c, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), c, _x43), X3)
mark#(if(X1, if(f(if(c, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(c, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(c, mark(_x102), _x103), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x81, f(_x111), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x111)), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(c, if(f(if(c, if(_x91, _x92, _x93), _x83)), false, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), false, _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(c), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(c), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(false), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(false), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(false, _x32, _x33), X3)) → a__if#(mark(X1), a__if(false, mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), true, _x43), X3)) → a__if#(mark(X1), if(a__f(true), true, _x43), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(f(_x111)), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(a__f(mark(_x111))), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), c, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(mark(c), c, f(true))), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), c, _x43), X3)mark#(if(c, if(f(if(c, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(true, if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(true, if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, false, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)
mark#(if(f(f(_x51)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(if(_x21, c, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), c, _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(if(true, f(false), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(true, a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, c, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, c, _x73), _x33), X3)mark#(if(f(if(_x51, f(if(c, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(c, c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(c, if(f(if(c, false, _x83)), false, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(c, false, _x83)), c, f(true)), false, _x43), X3)
mark#(if(if(_x21, _x22, _x33), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(if(mark(_x21), mark(_x22), _x33), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x51, f(if(f(_x91), c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(a__f(mark(_x91)), c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(true, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(true, a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)mark#(if(if(if(_x41, c, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), c, _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(true, if(f(true), _x32, _x43), X3)) → a__if#(true, if(a__f(true), mark(_x32), _x43), X3)mark#(if(if(_x21, f(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83))), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x51, f(if(false, false, _x83)), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(a__f(a__f(c)), if(if(c, c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)
mark#(if(f(if(if(_x61, _x62, _x63), f(false), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(f(_x41), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(c, if(f(if(c, _x82, _x73)), c, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, _x62, _x73), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x43), X3)mark#(if(if(if(_x41, _x42, _x43), true, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), true, _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, f(_x71), _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__f(mark(_x71)), _x63), _x43), X3)mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(mark(c), f(_x61), f(true))), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x33), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x33), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(if(_x21, c, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), c, _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(c, mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(if(_x51, f(if(false, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(c, c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x33), X3)mark#(if(f(if(true, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(true, mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(f(f(_x61)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__f(mark(_x61))))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(a__f(mark(_x91)), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(if(_x51, f(if(f(_x91), _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(a__f(mark(_x91)), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(false, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x53), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(if(mark(_x41), mark(_x42), _x53), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, false, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(if(_x21, true, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), true, _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), f(_x31), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__f(mark(_x31)), X3)mark#(if(if(true, _x22, _x23), if(f(if(if(_x71, _x72, _x73), f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(a__if(mark(_x71), mark(_x72), _x73), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(X1, if(f(c), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(if(_x111, _x112, _x113), true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(a__if(mark(_x111), mark(_x112), _x113), true, _x93), c, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(f(false), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(_x51, f(f(_x81)), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__f(mark(_x81))), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(true), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(true), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(if(mark(if(a__f(mark(_x61)), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(c), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), true, _x43), X3)
mark#(if(if(_x21, false, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), false, _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(if(false, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(false, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(c, if(f(if(c, f(_x111), _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, a__f(mark(_x111)), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(if(_x51, f(false), _x43)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(if(mark(_x51), a__f(false), _x43)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(false, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(X1, f(c), X3)) → a__if#(mark(X1), a__f(c), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(if(mark(_x81), false, _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, c, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)mark#(if(X1, if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), true, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), true, _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(mark(_x91)), c, f(true)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), if(_x51, _x52, _x53), _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(if(c, f(false), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(false), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(X1, if(f(c), if(c, c, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(c), if(c, c, _x73), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)
mark#(if(c, f(false), X3)) → a__if#(c, a__f(false), X3)mark#(if(if(true, _x22, _x23), if(f(if(f(_x91), f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(a__f(mark(_x91)), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(c, c, f(true)), true, _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(if(_x111, _x112, _x113)), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(a__if(mark(_x111), mark(_x112), _x113)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(true, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(true, a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(c, c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(X1, if(f(c), if(false, _x62, _x71), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), mark(_x71), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(c), if(_x61, c, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x43), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(false), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(false), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, true, X3)) → a__if#(mark(X1), true, X3)
mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(c, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, c, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), c, _x83), c, _x63), _x33), X3)
mark#(if(if(true, false, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, false, _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, c, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), c, _x103), _x73), _x33), X3)
mark#(if(f(if(false, f(false), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(false, a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, f(_x111), _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), a__f(mark(_x111)), _x103), _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(if(mark(_x81), a__f(mark(_x91)), _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(false, if(f(if(c, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(false), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, true, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(c, if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), true, _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, if(_x121, _x122, _x123), _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), a__if(mark(_x121), mark(_x122), _x123), _x93), c, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), false, _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, _x62, _x73), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x43), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__if(mark(mark(_x61)), c, f(true)), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(c, if(f(c), if(c, _x62, _x63), _x43), X3)) → a__if#(c, if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)mark#(if(f(if(_x51, f(if(_x81, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(true, if(c, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(c, mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(c, c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, true), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, false, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(a__f(false), false, _x63), true, _x43))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, f(if(_x81, _x82, _x83)), _x23), if(f(c), if(mark(if(_x81, _x82, _x83)), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(f(true))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, f(_x101), _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(c, a__f(mark(_x101)), _x73), _x33), X3)mark#(if(f(c), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(_x71), mark(_x72), _x73), mark(_x62), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__if(mark(mark(_x91)), c, f(true)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(true), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(true), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(if(c, if(_x111, _x112, _x113), _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, a__if(mark(_x111), mark(_x112), _x113), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, f(_x91), _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(false, if(_x31, _x32, _x33), X3)) → a__if#(false, a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(if(f(_x81), _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__f(mark(_x81)), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__if(mark(mark(_x61)), c, f(true)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(if(true, if(_x51, c, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), c, _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(c), c, f(true))), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), false, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, false, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(c, c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, false, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, false, _x63), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), f(mark(_x91)), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, false, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), if(false, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(false, true, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(_x61, c, _x63), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x43), X3)
mark#(if(if(_x21, c, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), c, _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(false)), c, f(true)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(c, if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), if(c, if(_x71, _x72, _x73), _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), a__if(c, a__if(mark(_x71), mark(_x72), _x73), _x63), _x43), X3)mark#(if(if(true, if(c, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(c, mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(false, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, mark(_x102), _x103), _x73), _x33), X3)mark#(if(f(f(f(f(_x61)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__f(mark(_x61))))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), a__f(mark(_x61)), _x33), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(X1, if(f(f(_x81)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__f(mark(_x81))), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__if(mark(mark(_x91)), c, f(true)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x93)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(if(mark(_x81), mark(_x82), _x93)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(if(_x41, _x42, _x43)), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), false, _x63), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(true, mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, if(_x111, _x112, _x113), _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), a__if(mark(_x111), mark(_x112), _x113), _x83), c, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(a__f(false), false, _x53), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(c), if(f(_x81), c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), c, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), if(mark(_x101), mark(_x102), _x113), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), if(if(if(_x101, _x102, _x103), _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(a__if(mark(_x101), mark(_x102), _x103), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(if(f(_x61), f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(mark(_x61)), a__if(mark(false), c, f(true)), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(if(if(_x41, true, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), true, _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
a__if#(true, X, Y) → mark#(X)mark#(if(if(true, if(f(_x71), _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(a__f(mark(_x71)), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(true, if(_x51, true, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), true, _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, c, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), c, _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(if(true, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(true, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(true, if(f(_x51), _x32, _x43), X3)) → a__if#(true, if(a__f(mark(_x51)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(c), if(false, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(false, c, _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, c, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(f(if(true, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(true, a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), if(a__if(mark(_x81), mark(_x82), _x83), c, _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(if(_x21, f(f(_x71)), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(a__f(mark(_x71))), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(f(a__f(a__f(mark(_x51)))), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(true, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(true, false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), true, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(f(_x111), true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(a__f(mark(_x111)), true, _x93), c, _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(_x61, c, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(mark(_x61), c, _x73), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), f(true), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(true), c, f(true)), _x33), X3)mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(f(f(false)), a__if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(if(_x51, f(if(_x81, f(_x91), _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(mark(_x81), a__f(mark(_x91)), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), c, f(true)), _x33), X3)) → a__if#(a__if(mark(_x21), if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, true, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), true, _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(if(_x21, true, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), true, _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(f(if(_x51, f(if(_x81, false, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), false, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(c, if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(c, if(f(if(c, true, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, true, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(true), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), f(_x71), _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), a__f(mark(_x71)), _x43), X3)
mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, c), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)mark#(if(if(f(_x41), f(_x51), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(f(_x41), _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(true, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(true, mark(_x102), _x103), _x73), _x33), X3)
mark#(if(X1, if(f(if(c, true, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, true, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(mark(_x51)), c, f(true))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(c, if(f(if(c, false, _x83)), false, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, false, _x83)), c, f(true)), false, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(f(_x111)), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(a__f(mark(_x111))), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(mark(_x91)), c, f(true)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(if(if(_x61, _x62, _x63), f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x43))), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(c)), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(f(_x91), _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), if(if(if(_x71, _x72, _x73), true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(c, c, f(true)), a__if(if(a__if(mark(_x71), mark(_x72), _x73), true, _x93), c, _x63), _x43), X3)
mark#(if(f(true), if(f(c), if(if(c, true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(c, true, _x93), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, f(_x31), X3)) → a__if#(mark(X1), f(mark(_x31)), X3)mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(true, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(true, false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, false, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), false, _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__if(mark(false), c, f(true)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), false, _x43), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(false), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(false, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), f(_x51), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, f(_x121), _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), a__f(mark(_x121)), _x93), c, _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(c), c, f(true))), a__if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(f(f(f(if(if(_x71, _x72, _x73), _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(a__if(mark(_x71), mark(_x72), _x73), mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x51)), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(if(true, if(_x51, false, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), false, _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(c)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(if(_x51, f(if(_x81, f(_x91), _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), a__f(mark(_x91)), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(true, if(c, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(c, mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(true, f(if(_x81, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(true, a__f(a__if(mark(_x81), c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, f(false), _x23), if(f(c), if(mark(false), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(false), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, c), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(mark(_x61)), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)
mark#(if(X1, if(f(c), if(c, _x62, _x73), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x43), X3)mark#(if(f(if(_x51, f(if(if(_x91, _x92, _x93), c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(a__if(mark(_x91), mark(_x92), _x93), c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(true, if(f(c), if(c, _x62, _x63), _x43), X3)) → a__if#(true, if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x43), X3)mark#(if(if(true, if(_x51, if(_x81, _x82, _x83), _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), a__if(mark(_x81), mark(_x82), _x83), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), mark(_x62), _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, true, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(c, true, _x63), _x33), X3)mark#(if(true, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__if(mark(c), c, f(true)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, X2, X3)) → a__if#(true, mark(X2), X3)mark#(if(f(f(c)), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(c, c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, if(_x51, _x52, _x53), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, f(_x101), _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, a__f(mark(_x101)), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, _x102, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(f(_x21), if(f(true), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(if(_x51, f(if(_x81, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, c, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), c, _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(if(_x51, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__f(mark(_x51)))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, c), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(f(mark(_x71)), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__if(mark(f(true)), c, f(true)), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(f(_x111)), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(a__f(mark(_x111))), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(true), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(true), mark(_x32), _x43), X3)mark#(if(if(true, if(_x51, f(_x81), _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), a__f(mark(_x81)), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(a__f(mark(_x51)))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, f(c), _x23), if(f(c), if(mark(c), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(c), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(f(_x91), false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(a__f(mark(_x91)), false, _x103), _x73), _x33), X3)mark#(if(X1, f(f(_x51)), X3)) → a__if#(mark(X1), a__f(a__f(mark(_x51))), X3)
mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__f(mark(_x71)), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(f(_x91), _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(a__f(mark(_x91)), mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x43), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(if(_x21, c, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), c, _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)mark#(if(if(if(c, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(c, mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(if(_x81, _x82, _x83), _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, c, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, if(_x111, _x112, _x113), _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), a__if(mark(_x111), mark(_x112), _x113), _x83), c, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, true), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), a__if(mark(_x71), mark(_x72), _x73), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(false, if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(a__f(false), false, _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(mark(_x61)), c, f(true)), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(true, if(_x31, true, _x33), X3)) → a__if#(true, a__if(mark(_x31), true, _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), false, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), false, _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(false, if(f(if(_x71, c, _x73)), c, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), f(f(_x81)), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__f(a__f(mark(_x81))), _x33), X3)
mark#(if(c, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, f(_x91)), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__f(mark(_x91)), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, if(_x101, _x102, _x103), _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(false, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(false, mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(if(mark(_x81), a__f(mark(_x91)), _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(false), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(true), c, f(true)), if(if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x43), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(_x21, f(mark(c)), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(c, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), c, _x53))), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), if(a__if(c, c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x43), X3)mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(if(if(c, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(c, mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(f(mark(_x61)), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(false, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(false, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(if(true, if(true, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(true, mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), f(mark(_x61)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(if(f(_x61), f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(false, c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(false, c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(c), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x83), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(mark(_x101), false, _x83), _x73), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(f(_x111)), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(a__f(mark(_x111))), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, c, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(c), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(c)), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__f(f(c)), a__if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(f(false), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(false), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(c, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(if(c, true, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, true, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), true, _x33), X3)mark#(if(f(if(false, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(false, f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, f(_x91), _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(mark(_x61), a__f(mark(_x91)), _x73), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(mark(_x91), f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__if(mark(mark(_x91)), c, f(true)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(f(f(c)), if(f(c), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(mark(_x61), mark(_x62), _x53), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(if(_x41, _x42, _x43), f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(if(true, if(false, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(false, mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(mark(_x61)), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(c, if(f(c), if(false, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)
mark#(if(f(c), if(f(c), if(c, if(f(_x91), false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__f(mark(_x91)), false, _x103), _x73), _x33), X3)mark#(if(f(false), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(false), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(if(true, _x22, _x31), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(mark(_x22)), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x63)), if(true, a__f(mark(_x91)), _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(if(mark(_x81), a__f(mark(_x91)), _x63)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(if(if(_x41, _x42, _x53), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(if(mark(_x41), mark(_x42), _x53), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(if(c, _x82, _x63)), false, _x43), X3)) → a__if#(c, if(a__if(mark(if(c, mark(_x82), _x63)), c, f(true)), false, _x43), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(a__f(false), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, _x22, _x33), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(if(mark(_x21), mark(_x22), _x33), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, f(_x91), _x63), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x43), X3)
mark#(if(if(if(true, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(true, mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(if(c, c, _x83)), false, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(c, c, _x83)), c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(c, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(c, mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, c, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(a__f(false), mark(_x62), _x63), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(true), if(f(c), if(c, if(false, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(true), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(c), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(false, if(f(if(true, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(true, c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(a__f(false), mark(_x62), _x63), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(if(if(f(_x61), _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(a__f(mark(_x61)), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(true, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), f(true), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__f(true), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(f(a__f(false)), if(if(mark(c), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(_x61, _x62, _x63), _x43), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(a__if(mark(_x91), mark(_x92), _x93), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(true), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), false, _x33), X3)mark#(if(false, if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(if(c, c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(X1, if(f(c), if(false, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(false, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x83), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(mark(_x101), false, _x83), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, f(c), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(c), _x63), _x33), X3)
mark#(if(if(if(_x41, c, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), c, _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(a__f(mark(_x71))), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(X1, if(f(_x51), if(_x81, _x82, _x83), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__if(mark(_x81), mark(_x82), _x83), _x43), X3)mark#(if(c, if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(c, if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, false, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)mark#(if(f(f(f(false))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(false))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(if(c, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(c, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(c), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(if(_x51, f(true), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(true), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(mark(_x61)), f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(if(_x111, _x112, _x113)), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(a__if(mark(_x111), mark(_x112), _x113)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(if(_x61, _x62, _x63), f(false), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(false, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, if(_x91, _x92, _x93)), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x91), mark(_x92), _x93), _x73), _x33), X3)mark#(if(f(if(_x51, _x52, _x43)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(if(mark(_x51), mark(_x52), _x43)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(if(true, true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(mark(c), c, f(true)), a__if(if(true, true, _x93), c, _x63), _x43), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(c, c, f(true)), false, _x33), X3)mark#(if(f(c), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, false, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), false, _x93), c, _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x43), X3)) → a__if#(c, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(false, if(f(c), if(false, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, false), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(f(false), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(false), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(if(false, true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(mark(c), c, f(true)), a__if(if(false, true, _x93), c, _x63), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(c)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, _x62, _x63), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), c, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(c)), if(f(c), c, _x43), X3)) → a__if#(a__f(a__f(c)), if(if(c, c, f(true)), c, _x43), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)mark#(if(f(f(false)), if(f(c), f(_x71), _x43), X3)) → a__if#(f(a__f(false)), if(if(mark(c), c, f(true)), a__f(mark(_x71)), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), c, _x33), X3)
mark#(if(f(if(c, f(false), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(false, a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(true, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(if(_x51, f(false), _x43)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(mark(_x51), a__f(false), _x43)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(f(_x111), _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(a__f(mark(_x111)), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), false, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), c, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), c, _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(false), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(false), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(c), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), true, _x33), X3)
mark#(if(f(if(_x51, f(if(true, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(true, mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), false, _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(c, if(f(true), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), c, f(true)), _x33), X3)) → a__if#(a__if(mark(_x21), if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x33), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(if(true, a__if(mark(_x51), mark(_x52), _x53), _x33), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(c, f(false), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(c, if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(c, _x82, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, c, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), c, _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(a__f(false), false, _x63), true, _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(if(_x51, f(if(_x81, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(mark(_x81), c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(false, if(f(true), _x32, _x43), X3)) → a__if#(false, if(a__f(true), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(c, c, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(c, c, _x33), X3)mark#(if(X1, if(f(if(_x81, if(_x111, _x112, _x113), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), a__if(mark(_x111), mark(_x112), _x113), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(if(c, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(c, a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(if(false, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(false, a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(c, c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(c, c, _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(_x31, if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(c, c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(true, c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(true, c, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x43), X3)) → a__if#(f(a__f(false)), if(if(mark(c), c, f(true)), c, _x43), X3)mark#(if(c, if(f(if(c, _x82, _x73)), true, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), true, _x33), X3)
mark#(if(f(f(true)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(if(_x21, f(mark(c)), _x23), if(f(c), if(mark(mark(c)), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, _x62, _x63), _x43), X3)) → a__if#(a__f(a__f(c)), if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x43), X3)mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)mark#(if(if(_x21, false, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), false, _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__if(mark(a__if(mark(false), c, f(true))), c, f(true)), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(false), mark(_x32), _x33), X3)
mark#(if(f(if(_x51, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(false, mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), c, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), c, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(true), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(f(_x91), _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__f(mark(_x91)), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(false, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(false, a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(if(true, true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(true, true, _x93), c, _x63), _x33), X3)mark#(if(f(c), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(if(true, if(_x51, if(_x81, _x82, _x83), _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), a__if(mark(_x81), mark(_x82), _x83), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(c, _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(c, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), if(c, c, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), a__if(c, c, _x63), _x43), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(if(_x51, f(if(_x81, false, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(mark(_x81), false, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x43), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(false, true, _x33), X3)) → a__if#(mark(X1), a__if(false, true, _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(if(_x21, f(false), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(false), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, false), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(mark(_x61)), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(c, false, _x73), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), if(a__if(c, c, f(true)), if(c, if(c, false, _x73), _x73), _x43), X3)
mark#(if(f(f(false)), if(f(c), f(_x71), _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), a__f(mark(_x71)), _x43), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(false), _x53)), c, f(true)), a__if(if(c, c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(a__f(false), false, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(_x31, c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), c, _x33), X3)
mark#(if(X1, if(f(c), if(false, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(false, false, _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), f(_x51), _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(true), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(if(_x51, f(if(_x81, if(_x91, _x92, _x93), _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(false), c, f(true)), a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), if(if(true, f(_x111), _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, a__f(mark(_x111)), _x83), c, _x63), _x33), X3)
mark#(if(X1, if(_x31, true, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), true, _x43), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(if(if(_x41, if(_x71, _x72, _x73), _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), a__if(mark(_x71), mark(_x72), _x73), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(X1, if(f(if(_x81, true, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(false), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(false), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(true), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(true), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), false, _x53))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(if(_x51, f(if(f(_x91), _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(a__f(mark(_x91)), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, true, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), true, _x33), X3)
mark#(if(f(if(_x51, f(c), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(c), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(X1, if(f(_x51), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(true, _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(true, mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(c), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(c), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(true), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(false, if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(if(_x91, _x92, _x93), false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__if(mark(_x91), mark(_x92), _x93), false, _x103), _x73), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(if(mark(_x81), false, _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(true, c, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(true, c, _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x33), X3)mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(false), if(f(c), _x32, _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(false), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(false), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), f(_x61), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(mark(_x61)), c, f(true)), _x43), X3)mark#(if(c, if(f(if(c, _x82, _x83)), true, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), true, _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), f(false), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__f(false), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x43), X3)) → a__if#(a__if(mark(if(a__f(mark(_x61)), a__f(false), _x43)), c, f(true)), if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x43), X3)
mark#(if(f(f(false)), if(f(c), f(_x71), _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), a__f(mark(_x71)), _x43), X3)mark#(if(f(if(_x51, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(if(mark(a__if(mark(_x51), f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x33), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(if(mark(_x21), mark(_x22), _x33), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, if(false, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(X1, if(f(c), if(false, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(false, a__f(mark(_x91)), _x63), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x31), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(a__if(mark(_x51), mark(_x52), _x53)), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), true, _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), f(_x71), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__f(mark(_x71)), _x43), X3)
mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x83), c, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(a__if(true, mark(_x82), _x83), c, _x73), _x33), X3)mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), true, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(c), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, if(_x51, _x52, _x53), _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(if(if(_x61, _x62, _x63), f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), false, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(if(_x91, _x92, _x93), _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x102), _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), mark(_x72), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(f(f(if(true, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(true, mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(true)), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(if(true, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(false, c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(false, c, _x63), _x33), X3)
mark#(if(if(_x21, true, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), true, _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), c, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(false, true, X3)) → a__if#(false, true, X3)
mark#(if(f(f(mark(c))), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(X1, if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(a__if(mark(_x61), mark(_x62), _x63)), c, f(true)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(c, X2, X3)) → a__if#(c, mark(X2), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(false, a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(f(_x91), f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(a__f(mark(_x91)), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(if(_x61, _x62, _x63), _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(c, if(f(if(c, false, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, false, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x61, _x62, _x63))), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(a__if(mark(_x61), mark(_x62), _x63))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, c, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x43), X3)
mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(if(false, _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(false, mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(f(if(_x61, c, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), c, _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(if(true, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(true, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(c)), if(f(c), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, false, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)mark#(if(f(if(_x51, f(if(_x81, c, _x83)), _x43)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(if(mark(_x51), a__f(a__if(mark(_x81), c, _x83)), _x43)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, true), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(mark(_x61)), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(c, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(c, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(mark(_x41))), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(true, if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(false, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(false, false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, f(_x51), _x33), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x33), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, true, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, true, _x63), _x43), X3)
mark#(if(if(true, if(_x51, f(_x81), _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), a__f(mark(_x81)), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(if(_x91, _x92, _x93), f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x33), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(if(true, a__if(mark(_x51), mark(_x52), _x53), _x33), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x43), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x43), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, true), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(if(mark(c), c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(c, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, c, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(c), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(false, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(false, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(if(if(false, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(false, mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(X1, if(f(c), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(if(f(_x61), f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), f(mark(_x61)), _x33), X3)
mark#(if(c, if(f(if(c, c, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, c, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(false, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(false, a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, true, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, true, _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(true), c, _x43), X3)) → a__if#(mark(X1), if(a__f(true), c, _x43), X3)
mark#(if(if(f(_x41), f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, true, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(X1, if(f(c), if(c, false, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(c, false, _x63), _x33), X3)
mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, f(_x101), _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, a__f(mark(_x101)), _x73), _x33), X3)
mark#(if(f(f(if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(mark(_x41))), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(a__f(true))), c, f(true)), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(c, if(f(if(c, if(_x91, _x92, _x93), _x83)), false, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), false, _x43), X3)
mark#(if(false, if(f(if(f(_x91), c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(a__f(mark(_x91)), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(c, c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(true), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), f(_x61), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__f(mark(_x61)), _x43), X3)
mark#(if(X1, if(f(if(if(_x81, _x82, _x83), c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x73)), mark(_x32), _x33), X3)mark#(if(true, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(true, if(if(_x71, _x72, _x73), _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(a__if(mark(_x71), mark(_x72), _x73), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(a__if(mark(_x81), mark(_x82), _x83), c, _x73), _x33), X3)
mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, if(_x91, _x92, _x93)), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x91), mark(_x92), _x93), _x73), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, true, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(false)), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(true, c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(a__f(mark(_x81))), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), mark(_x52), _x53))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(false, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(true), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), if(mark(mark(_x61)), c, f(true)), _x33), X3)
mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(if(if(_x41, c, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), c, _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x33), X3)mark#(if(f(if(f(_x61), _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(c), if(f(c), if(c, if(c, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(c, false, _x103), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(true, if(_x51, c, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), c, _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), if(a__if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x43), X3)
mark#(if(X1, if(true, true, _x33), X3)) → a__if#(mark(X1), a__if(true, true, _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(c, a__f(mark(_x91)), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(if(_x51, f(f(_x81)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__f(mark(_x81))), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(if(_x41, c, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), c, _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, _x62, _x63), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(f(f(true)), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(false, f(_x31), X3)) → a__if#(false, a__f(mark(_x31)), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(false), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(false), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(c), if(true, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(true, c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(f(false), a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), mark(_x72), _x73), _x63), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), true, _x33), X3)
mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__if(mark(mark(_x61)), c, f(true)), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(c, if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x63), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, mark(_x52), _x63), _x33), X3)) → a__if#(a__if(true, if(mark(_x51), mark(_x52), _x63), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), true, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), true, _x43), X3)
mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x43), X3)) → a__if#(a__f(a__f(c)), if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x33), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x33), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), f(if(_x81, _x82, _x83)), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x73), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), if(if(mark(_x81), true, _x93), c, _x73), _x33), X3)
mark#(if(c, f(_x31), X3)) → a__if#(c, a__f(mark(_x31)), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(mark(_x41))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(X1, if(f(c), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), a__f(mark(_x71)), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(f(_x41), _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(c)), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)mark#(if(f(true), if(f(c), if(if(f(_x71), true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(c, c, f(true)), a__if(if(a__f(mark(_x71)), true, _x93), c, _x63), _x43), X3)
mark#(if(X1, if(f(_x51), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x73)), _x32, _x43), X3)) → a__if#(c, if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), mark(_x32), _x43), X3)mark#(if(if(c, f(_x51), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(c, a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(_x91), _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), false, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(if(c, c, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(c))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__if(mark(mark(_x61)), c, f(true)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(if(_x91, _x92, _x93), false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), mark(_x72), _x73), _x63), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, c), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(a__f(mark(_x121)), mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, f(_x101), _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, a__f(mark(_x101)), _x73), _x33), X3)mark#(if(f(true), if(f(c), if(if(true, true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(true, true, _x93), c, _x63), _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(c, a__if(if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__if(mark(mark(_x91)), c, f(true)), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(true), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(true), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(c, if(c, c, _x33), X3)) → a__if#(c, a__if(c, c, _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(if(if(false, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(false, mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x43), X3)) → a__if#(a__f(f(false)), if(if(mark(c), c, f(true)), a__f(mark(_x61)), _x43), X3)
mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x33), X3)mark#(if(if(_x21, if(_x51, _x52, _x53), _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), a__f(mark(_x61)), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(if(c, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(c, a__f(mark(_x61)), _x53)), c, f(true)), if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x43), X3)mark#(if(f(_x21), if(f(c), if(if(false, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(false, mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(false, if(f(if(false, c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(false, c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(mark(_x91)), c, f(true)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(c, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(_x71), mark(_x72), _x73), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, false, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(true), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(c, if(_x31, c, _x33), X3)) → a__if#(c, a__if(mark(_x31), c, _x33), X3)mark#(if(X1, if(f(c), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(f(_x61), f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(true), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(c), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), f(if(_x91, _x92, _x93)), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(a__if(mark(_x91), mark(_x92), _x93)), c, f(true)), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(if(_x111, _x112, _x113)), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(a__if(mark(_x111), mark(_x112), _x113)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x71, f(_x81), _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), a__f(mark(_x81)), _x73)), mark(_x32), _x33), X3)
mark#(if(if(_x21, false, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), false, _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x61, true, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(if(_x111, _x112, _x113)), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(a__if(mark(_x111), mark(_x112), _x113)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(true, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(true, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(if(if(_x41, _x42, _x53), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(if(mark(_x41), mark(_x42), _x53), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(if(true, if(f(_x71), _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(a__f(mark(_x71)), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), f(f(_x91)), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(a__f(mark(_x91))), c, f(true)), _x33), X3)mark#(if(if(c, _x22, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(c, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), f(false), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(false), c, f(true)), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(true, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(true, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(a__if(mark(_x81), mark(_x82), _x83)), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(if(_x51, f(if(true, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(true, c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(true, mark(_x62), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(false, if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(true, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), false, _x43))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), if(_x71, _x72, _x73), _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(c), if(c, _x62, _x63), f(true)), X3)) → a__if#(mark(X1), if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x43), X3)
mark#(if(if(if(if(_x61, _x62, _x63), _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(false), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(mark(_x51)), c, f(true)))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(if(_x21, f(false), _x23), if(f(c), if(mark(false), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(false), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x53), _x43), X3)) → a__if#(f(true), if(a__if(c, c, f(true)), if(if(mark(_x81), true, _x93), c, _x53), _x43), X3)mark#(if(c, if(f(if(c, _x82, _x73)), f(_x61), _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, mark(_x82), _x73)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(f(_x81), c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__f(mark(_x81)), c, _x73)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(mark(_x51), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(true, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(_x21), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), c, _x43), X3)mark#(if(if(c, _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(c, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)
mark#(if(if(c, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(c, a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(false)), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(false, if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(c), if(c, _x62, _x53), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x53), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), a__if(mark(_x131), mark(_x132), _x133), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x71, _x72, _x73), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(c, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(true), c, f(true)))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(true, if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x43), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x43), X3)mark#(if(f(_x21), if(f(c), if(if(if(_x111, _x112, _x113), _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(a__if(mark(_x111), mark(_x112), _x113), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(if(c, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, if(_x71, _x72, _x73), _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__if(mark(_x71), mark(_x72), _x73), _x63), _x43), X3)
mark#(if(if(true, if(true, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(true, mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), X2, X3)) → a__if#(a__f(mark(_x21)), mark(X2), X3)
mark#(if(if(_x21, c, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), c, _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, f(true), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(true), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), true, _x43), X3)) → a__if#(a__f(a__f(c)), if(if(c, c, f(true)), true, _x43), X3)mark#(if(f(if(_x51, f(if(_x81, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), c, _x83)), _x53)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x43), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), f(true)), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(f(f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(false), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(false), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(c, if(f(if(c, true, _x83)), false, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(c, true, _x83)), c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, f(false), X3)) → a__if#(mark(X1), a__if(mark(false), c, f(true)), X3)
mark#(if(c, if(_x31, _x32, _x33), X3)) → a__if#(c, a__if(mark(_x31), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(true, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(true, false, _x103), _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(if(if(_x61, _x62, _x63), f(if(_x81, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(a__if(mark(_x81), c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(if(c, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(c), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(c), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x51, f(if(false, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(false, mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x32), _x43), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(a__f(mark(_x51)))), c, f(true)), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(X1, if(f(_x51), true, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), true, _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), f(_x51), _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(false, c, X3)) → a__if#(false, c, X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__if(mark(_x61), mark(_x62), _x63), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), false, _x53))), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(if(false, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(false, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(true)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(false, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x93), c, _x73), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), if(if(mark(_x81), mark(_x82), _x93), c, _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(mark(_x101), false, _x83), _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(c, c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(if(true, if(_x51, true, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), true, _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(c, c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, c, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(true, if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(mark(_x61)), c, f(true)), _x33), X3)mark#(if(if(if(_x41, f(_x71), _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), a__f(mark(_x71)), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, false), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(f(c), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(c), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(true, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(true, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, f(if(_x51, _x52, _x53)), X3)) → a__if#(mark(X1), a__f(a__if(mark(_x51), mark(_x52), _x53)), X3)mark#(if(if(if(c, _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(c, mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), false, _x63), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, c, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), c, _x83), c, _x63), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), false, _x33), X3)mark#(if(if(true, _x22, _x33), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(if(true, mark(_x22), _x33), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(if(if(if(_x61, _x62, _x63), _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, c, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, c, _x63), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), c, _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(false, f(if(_x81, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(false, a__f(a__if(mark(_x81), c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(f(true))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(a__f(true))), if(a__if(c, c, f(true)), c, _x43), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(if(_x51, _x52, _x53), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), mark(_x32), _x33), X3)
mark#(if(if(f(_x41), _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x43), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), c, _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(if(f(_x41), _x22, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), a__f(mark(_x71)), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(true), if(f(c), if(if(false, true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(false, true, _x93), c, _x63), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, true, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(false, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), a__if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(true, mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x71, c, _x63)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(if(mark(_x71), c, _x63)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, c, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(f(true), if(f(c), if(if(c, true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(c, c, f(true)), a__if(if(c, true, _x93), c, _x63), _x43), X3)
mark#(if(if(if(_x41, f(_x71), _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), a__f(mark(_x71)), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), if(c, c, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(c, c, _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(f(_x81), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), c, _x63), _x33), X3)mark#(if(f(true), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(if(true, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(true, _x22, _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x61))), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(a__f(mark(_x61)))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(if(_x51, f(if(_x81, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(f(_x91), f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(a__f(mark(_x91)), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(c), _x32, _x33), X3)) → a__if#(c, a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(if(if(c, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(c, mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), true, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), true, _x43), X3)
mark#(if(if(_x21, true, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), true, _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(f(_x81), f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(f(_x91), false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(a__f(mark(_x91)), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), true, _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(true))), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(f(false), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(false), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(if(_x21, if(_x51, _x52, _x53), _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(if(f(_x101), _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__f(mark(_x101)), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(c, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(c, false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(false, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(false, false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(if(_x61, _x62, _x63), f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x63)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(if(mark(_x71), mark(_x72), _x63)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(c, mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(mark(_x51), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(c, f(c), _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(c, f(c), _x73)), c, f(true)), a__if(mark(mark(_x61)), c, f(true)), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), f(f(_x81)), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__f(a__f(mark(_x81))), _x33), X3)mark#(if(f(_x21), if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, c, _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(if(false, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(false, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(f(a__f(false)), if(if(c, c, f(true)), true, _x43), X3)mark#(if(f(_x21), if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(c, f(true), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(true), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), true, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), f(c), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__f(c), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(f(false), false, _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(if(_x81, _x82, _x83), f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x31), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(a__if(mark(_x51), mark(_x52), _x53)), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(f(_x61), f(if(_x81, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(a__if(mark(_x81), c, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(false, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(mark(c), f(_x61), f(true))), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(true), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(true), c, f(true)), a__if(if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__if(mark(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), c, f(true)), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(c), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(true, if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(true, if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(c, if(_x31, true, _x33), X3)) → a__if#(c, a__if(mark(_x31), true, _x33), X3)
mark#(if(if(f(_x41), _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x43), X3)mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x43), X3)) → a__if#(a__f(true), if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x43), X3)
mark#(if(if(_x21, true, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), true, _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), true, _x53))), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, f(f(_x81)), _x23), if(f(c), if(mark(f(_x81)), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(a__f(mark(_x81))), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(c), if(f(c), if(c, if(true, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(true, false, _x103), _x73), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x83), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(f(_x91), c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(if(_x51, f(if(_x81, true, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), true, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(if(c, true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(c, true, _x93), c, _x63), _x33), X3)mark#(if(if(true, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, a__f(mark(_x51)), _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, c, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), false, _x43), X3)) → a__if#(a__f(a__f(c)), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(false, f(false), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(false, a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(f(c))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(c))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(f(f(a__f(true))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x91), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(mark(mark(_x82)), c, _x63), _x33), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(true, _x22, _x33), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(if(true, mark(_x22), _x33), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x51, f(if(_x81, c, _x73)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(if(mark(_x81), c, _x73)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(true, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(c), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(if(true, if(false, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(false, mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), true, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), true, _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(if(false, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(false, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, true, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), true, _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), true, _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(a__f(false), mark(_x62), _x53), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), c, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, false, _x73), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(if(mark(c), c, f(true)), if(c, false, _x73), _x43), X3)mark#(if(if(_x21, f(if(_x71, _x72, _x73)), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(a__if(mark(_x71), mark(_x72), _x73)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(_x31, true, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), true, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(a__if(mark(_x121), mark(_x122), _x123), mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x71), c, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(if(_x41, f(_x71), _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), a__f(mark(_x71)), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), true, _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(c), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(c), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(c, mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(true, false, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, false, _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(X1, if(_x31, false, _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), false, _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(if(_x111, _x112, _x113)), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(a__if(mark(_x111), mark(_x112), _x113)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(false, if(_x31, c, _x33), X3)) → a__if#(false, a__if(mark(_x31), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(a__f(mark(_x51)))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), true, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), true, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x71, true, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), true, _x73)), mark(_x32), _x43), X3)mark#(if(f(true), if(f(c), if(if(if(_x111, _x112, _x113), _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(a__if(mark(_x111), mark(_x112), _x113), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), mark(_x62), _x63), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(f(mark(_x61)), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(X1, if(f(c), if(c, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(f(true), if(f(c), if(c, if(c, false, _x83), _x73), f(true)), X3)) → a__if#(if(mark(true), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(c, false, _x83), _x73), _x33), X3)
mark#(if(c, if(f(if(c, f(_x91), _x83)), false, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), false, _x43), X3)mark#(if(if(_x21, false, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), false, _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(_x61, false, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, true, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), true, _x83), c, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(if(_x51, f(if(_x81, c, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), c, _x83)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(false, mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(if(_x51, f(if(if(_x91, _x92, _x93), _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(true, f(_x31), X3)) → a__if#(true, a__f(mark(_x31)), X3)
mark#(if(X1, X2, X3)) → mark#(X1)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(false, f(false), X3)) → a__if#(false, a__f(false), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, true, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), f(false), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__f(false), _x33), X3)mark#(if(f(f(f(c))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(c))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), true, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), true, _x33), X3)mark#(if(f(if(_x51, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), true, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__f(mark(_x61)), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(true, _x32, _x33), X3)) → a__if#(mark(X1), a__if(true, mark(_x32), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, c, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(false), c, f(true)), false, _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(false, mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(f(if(c, f(true), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(true), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(c, if(f(if(c, c, _x83)), false, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, c, _x83)), c, f(true)), false, _x33), X3)mark#(if(f(true), if(f(c), if(if(c, true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(mark(c), c, f(true)), a__if(if(c, true, _x93), c, _x63), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), if(if(mark(c), c, f(true)), false, _x43), X3)mark#(if(if(true, _x22, _x31), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(mark(mark(_x22)), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(c), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(c), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(true), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(true, c, f(true)), if(a__if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x43), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, c, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)mark#(if(f(if(c, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__if(mark(mark(_x61)), c, f(true)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(X1, if(f(true), f(_x71), _x43), X3)) → a__if#(mark(X1), if(a__f(true), a__f(mark(_x71)), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(a__f(false), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(_x21, f(c), _x23), if(f(c), if(mark(c), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(c), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(X1, c, X3)) → a__if#(mark(X1), c, X3)mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(f(false), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x61, false, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)
mark#(if(X1, if(f(c), if(c, true, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), a__if(c, true, _x63), _x43), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), false, _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), c, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(X1, if(f(c), if(false, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), if(_x51, _x52, _x53), _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(if(_x21, f(if(_x81, _x82, _x83)), _x23), if(f(c), if(mark(if(_x81, _x82, _x83)), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(c), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(false), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(false), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(f(_x51))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), c, _x43), X3)mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, false), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(f(a__f(false)), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(f(_x111)), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(a__f(mark(_x111))), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(_x51), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(true), if(f(c), if(if(if(_x111, _x112, _x113), true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(a__if(mark(_x111), mark(_x112), _x113), true, _x93), c, _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, false, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(false), _x33), X3)
mark#(if(X1, if(f(if(c, f(f(_x111)), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(a__f(mark(_x111))), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(_x51), f(_x81), _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), a__f(mark(_x81)), _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(false, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(false, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x83), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(c), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__if(mark(mark(_x91)), c, f(true)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)mark#(if(c, if(f(if(c, _x82, _x83)), _x32, _x43), X3)) → a__if#(c, if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__if(mark(false), c, f(true)), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), c, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), c, _x43), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x71, false, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), false, _x73)), mark(_x32), _x43), X3)mark#(if(if(if(false, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(false, mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(c, a__f(c), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(a__f(mark(_x71)), mark(_x62), _x53), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(c), if(f(c), _x32, _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), true, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), true, _x43), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x93), c, _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(if(mark(_x81), mark(_x82), _x93), c, _x73), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, c, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x33), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(if(mark(_x21), mark(_x22), _x33), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(mark(c), f(if(_x81, c, _x83)), f(true))), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), c, _x83)), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(c), if(f(c), if(c, if(if(_x91, _x92, _x93), false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__if(mark(_x91), mark(_x92), _x93), false, _x103), _x73), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(c, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(true, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(c, a__f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, true, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(false, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(false, a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), true, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(X1, if(f(c), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), false, _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), false, _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(if(c, c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(f(if(_x61, f(_x71), _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), a__f(mark(_x71)), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(_x91), _x71)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(mark(_x71)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(true, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(if(_x51, f(c), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(c), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(if(_x81, _x82, _x83)), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, f(false), X3)) → a__if#(mark(X1), f(false), X3)
mark#(if(if(if(f(_x61), _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(a__f(mark(_x61)), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(f(if(c, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(if(mark(a__if(c, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(true), if(f(c), _x32, _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x83)), false, _x33), X3)) → a__if#(c, a__if(if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), false, _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(f(_x91), f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(a__f(mark(_x91)), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, false, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)mark#(if(X1, if(f(if(if(_x101, _x102, _x103), _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__if(mark(_x101), mark(_x102), _x103), mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(c, c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(c, _x32, _x33), X3)) → a__if#(mark(X1), a__if(c, mark(_x32), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(a__f(mark(_x91)), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x51), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(mark(_x62)), _x43), X3)
mark#(if(X1, if(f(if(false, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(false, c, _x73)), mark(_x32), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, f(_x81), _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(a__f(mark(_x81))), _x33), X3)
mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__if(mark(false), c, f(true)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), false, _x63), true, _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(_x51, c, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), c, _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(c, mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(X1, if(f(if(f(_x91), _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, f(f(_x111)), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(a__f(mark(_x111))), _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(false, true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(false, true, _x93), c, _x63), _x33), X3)
mark#(if(f(_x21), if(_x31, true, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(mark(_x31), true, _x33), X3)mark#(if(if(if(_x41, false, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), false, _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), true, _x33), X3)mark#(if(X1, f(true), X3)) → a__if#(mark(X1), a__f(true), X3)
mark#(if(c, if(f(true), _x32, _x43), X3)) → a__if#(c, if(a__f(true), mark(_x32), _x43), X3)mark#(if(false, if(f(if(_x71, c, _x73)), false, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), false, _x33), X3)
mark#(if(if(if(_x41, false, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), false, _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(if(_x21, false, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), false, _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(false, _x22, _x23), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(a__if(false, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(true, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(true, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x51, if(_x61, _x62, _x63), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__if(mark(_x61), mark(_x62), _x63), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(f(a__if(mark(_x71), c, _x73)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x73)), if(true, _x62, mark(_x81)), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(if(mark(_x81), false, _x73)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(f(if(false, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(false, a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, false, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), false, _x83), c, _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), mark(_x62), _x63), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(_x21, f(c), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(c), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), true, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, true, _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(a__f(false), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(true, if(true, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(true, mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(f(mark(_x41))), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(if(_x21, f(f(_x71)), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(a__f(mark(_x71))), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(f(_x71), f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(a__f(mark(_x71)), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(f(if(_x51, f(if(_x81, false, _x83)), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, _x102, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(mark(_x101), mark(_x102), _x83), _x73), _x33), X3)
mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(f(a__f(true)), a__if(if(c, c, f(true)), c, _x33), X3)mark#(if(c, if(f(if(c, f(_x91), _x83)), false, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), false, _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(c, c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(mark(_x61)), a__f(false), _x43)), c, f(true)), a__if(if(c, c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(c, false, _x103), _x73), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(c, c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(false, if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, f(_x111), _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), a__f(mark(_x111)), _x83), c, _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(f(_x101), _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(a__f(mark(_x101)), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(if(c, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(f(f(false)), if(if(mark(c), c, f(true)), true, _x43), X3)
mark#(if(X1, if(f(c), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(c), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(f(_x101), c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__f(mark(_x101)), c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(if(true, _x22, _x31), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(mark(mark(_x22)), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), c, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), c, _x43), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(c)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, false, X3)) → a__if#(mark(X1), false, X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, if(_x91, _x92, _x93)), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x91), mark(_x92), _x93), _x73), _x33), X3)
mark#(if(X1, if(f(c), if(c, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(c, c, f(true)), a__if(c, mark(_x62), _x63), _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(f(f(_x51)), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)mark#(if(true, f(false), X3)) → a__if#(true, a__f(false), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(f(if(_x61, _x62, _x53)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(if(mark(_x61), mark(_x62), _x53)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(true, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(f(f(false)), if(f(c), f(_x71), _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), a__f(mark(_x71)), _x43), X3)mark#(if(X1, if(c, c, _x43), X3)) → a__if#(mark(X1), if(c, c, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(false), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, if(_x91, _x92, _x93)), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(mark(_x61)), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x91), mark(_x92), _x93), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(f(c), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)
mark#(if(f(if(_x51, f(if(_x81, _x82, _x83)), _x43)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(if(mark(_x51), f(a__if(mark(_x81), mark(_x82), _x83)), _x43)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, f(_x101), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__f(mark(_x101)), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, true, _x73), _x43), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x43), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(f(f(false)), if(f(c), f(true), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__f(true), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, false, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), false, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), mark(_x62), _x63), c, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(false), _x53)), c, f(true)), if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x43), X3)
mark#(if(X1, if(f(if(c, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(if(_x41, true, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), true, _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), false, _x33), X3)mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), false, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(true, mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(f(if(_x61, if(_x71, _x72, _x73), _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), a__if(mark(_x71), mark(_x72), _x73), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), false, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), false, _x43), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(_x51), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(c)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(if(_x51, _x52, _x53), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), c, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, true, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)
mark#(if(X1, if(f(f(_x81)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__f(mark(_x81))), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(if(c, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(c, a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(if(true, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(true, mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(f(_x91), _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(c, f(c), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(c), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x43), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(if(_x21, true, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), true, _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(if(_x91, _x92, _x93), false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x73), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), c, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), c, _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(false, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(false, false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(a__if(mark(_x81), mark(_x82), _x83)), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x71, if(_x81, _x82, _x83), _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), a__if(mark(_x81), mark(_x82), _x83), _x73)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, if(_x111, _x112, _x113), _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), a__if(mark(_x111), mark(_x112), _x113), _x103), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(c)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(f(true), if(f(c), if(if(f(_x71), true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(mark(c), c, f(true)), a__if(if(a__f(mark(_x71)), true, _x93), c, _x63), _x43), X3)mark#(if(f(c), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(c, c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x33), if(f(c), if(_x61, f(_x91), _x63), _x33), X3)) → a__if#(if(mark(_x21), mark(_x22), _x33), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(a__if(mark(a__f(mark(_x61))), mark(a__f(false)), _x33), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, false), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), _x33), X3)) → a__if#(f(true), a__if(if(mark(c), c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, f(_x91), _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(c, a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(false), c, f(true)), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(if(if(_x61, _x62, _x63), _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(c), if(false, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(false, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, true, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), true, _x103), _x73), _x33), X3)mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x53), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(if(mark(_x41), mark(_x42), _x53), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(mark(_x91)), c, f(true)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(a__f(false), false, _x63), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(a__if(a__f(mark(_x71)), mark(_x62), _x63), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, true, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(f(_x21), if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(f(false), false, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(c, _x82, _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), c, _x33), X3)mark#(if(f(f(_x51)), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(_x51), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(true, if(_x51, f(_x81), _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), a__f(mark(_x81)), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), X2, X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), mark(X2), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(false, if(f(c), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(if(_x91, _x92, _x93), _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(true, if(f(_x51), _x32, _x33), X3)) → a__if#(true, a__if(a__f(mark(_x51)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(f(false))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(false))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), true, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), false, _x33), X3)mark#(if(f(f(false)), if(f(c), true, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__f(mark(_x101)), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(_x21, f(_x51), _x33), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x33), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(true), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(true), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(if(_x51, f(if(c, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(c, mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(if(mark(a__if(a__f(mark(_x61)), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(c), if(c, f(_x71), _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), a__if(c, a__f(mark(_x71)), _x63), _x43), X3)
mark#(if(X1, if(f(_x51), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x43), X3)mark#(if(X1, if(f(_x51), c, _x43), X3)) → a__if#(mark(X1), if(a__f(mark(_x51)), c, _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(mark(_x61), mark(_x62), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), true, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, f(_x91)), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__f(mark(_x91)), _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), if(_x71, _x72, _x73), _x43), X3)) → a__if#(a__f(a__f(false)), if(if(mark(c), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x81, false, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(if(mark(c), f(if(_x81, _x82, _x83)), f(true))), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__f(mark(_x51)))), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(_x21), f(false), X3)) → a__if#(a__f(mark(_x21)), a__f(false), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(c)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x63), _x23), if(f(if(false, f(_x91), _x83)), if(true, mark(_x52), _x63), _x33), X3)) → a__if#(a__if(true, if(mark(_x51), mark(_x52), _x63), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(if(_x91, _x92, _x93), f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(false, if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(false, if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(f(if(c, f(_x61), _x43)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(if(c, a__f(mark(_x61)), _x43)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, if(_x121, _x122, _x123), _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), a__if(mark(_x121), mark(_x122), _x123), _x93), c, _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(c, c, f(true)), if(c, false, _x73), _x33), X3)
mark#(if(true, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, f(true), _x23), if(f(c), if(mark(true), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(true), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(true, if(_x31, c, _x33), X3)) → a__if#(true, a__if(mark(_x31), c, _x33), X3)mark#(if(f(if(_x51, f(if(c, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(c, mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(true, true, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, true, _x83), c, _x63), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, true), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(X1, if(f(true), _x32, _x43), X3)) → a__if#(mark(X1), if(f(true), mark(_x32), _x43), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x31), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(a__if(mark(_x51), mark(_x52), _x53)), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(false)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(if(mark(a__f(false)), c, f(true)), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(if(c, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(c, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x33), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(if(true, a__if(mark(_x51), mark(_x52), _x53), _x33), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(true)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(true)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(_x81, false, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), false, _x83), c, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(if(_x101, _x102, _x103), _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(a__if(mark(_x101), mark(_x102), _x103), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(_x21), if(f(true), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__f(true), mark(_x32), _x43), X3)
mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(true), mark(_x32), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x73), _x33), X3)) → a__if#(f(true), a__if(a__if(mark(c), c, f(true)), if(if(mark(_x81), true, _x93), c, _x73), _x33), X3)
mark#(if(f(if(mark(c), f(if(_x81, _x82, _x83)), f(true))), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), true, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(_x31, c, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), c, _x43), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), false, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), false, _x63), _x33), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(if(mark(_x81), a__f(mark(_x91)), _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x43), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), if(a__if(c, c, f(true)), c, _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(mark(_x61)), c, f(true)), _x33), X3)mark#(if(f(f(f(true))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(true))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(c)), if(f(c), true, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, if(_x91, _x92, _x93)), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x91), mark(_x92), _x93), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), _x32, _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(_x51), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(c, f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, _x22, _x33), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(if(mark(_x21), mark(_x22), _x33), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), c, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(c), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(true, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(true, mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(f(_x111), _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(a__f(mark(_x111)), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(true), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(true), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(X1, if(f(if(c, _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(c, mark(_x72), _x73)), mark(_x32), _x43), X3)
mark#(if(f(if(if(_x61, _x62, _x63), f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(mark(_x61)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), if(_x51, _x52, _x53), _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x51, true, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), true, _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x73)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(if(true, if(_x51, c, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), c, _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(c)), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(if(true, _x22, _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(false)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, c, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, true, _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(if(c, f(_x61), f(true))), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), a__if(if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(_x91), _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(if(false, a__f(mark(_x91)), _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(f(false), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, false, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, false, _x73), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)
mark#(if(f(f(f(_x51))), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x33), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x33), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(true, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(true, false, _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(if(c, _x82, _x83)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(f(mark(_x51)))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(false, if(f(if(_x71, c, _x73)), _x32, _x43), X3)) → a__if#(false, if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(a__f(a__f(false)), if(if(c, c, f(true)), true, _x43), X3)mark#(if(X1, if(f(if(c, f(if(_x111, _x112, _x113)), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(a__if(mark(_x111), mark(_x112), _x113)), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), a__if(a__if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), f(_x31), X3)) → a__if#(a__f(mark(_x21)), a__f(mark(_x31)), X3)mark#(if(f(_x21), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(true), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(c, if(f(if(c, _x82, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(if(mark(if(c, mark(_x82), _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), mark(_x52), _x43))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(c), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(c), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(if(f(_x61), _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(a__f(mark(_x61)), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x51, f(false), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(c, f(c), _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(_x91), _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(if(c, a__f(mark(_x91)), _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x73)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(mark(_x81), mark(_x82), _x73)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, if(_x71, _x72, _x73), _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), a__if(mark(_x71), mark(_x72), _x73), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(X1, X2, X3)) → mark#(X2)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), true, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), true, _x43), X3)mark#(if(false, if(f(true), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(true), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(if(_x51, f(if(_x81, false, _x83)), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(false, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(if(_x21, false, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), false, _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(f(f(mark(_x41))), if(if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(if(_x21, f(if(_x71, _x72, _x73)), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(a__if(mark(_x71), mark(_x72), _x73)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x43), X3)
mark#(if(c, if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(mark(_x61)), c, f(true)), _x33), X3)mark#(if(false, if(f(c), if(c, _x62, _x63), _x43), X3)) → a__if#(false, if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(if(_x91, _x92, _x93), false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(a__if(mark(_x91), mark(_x92), _x93), false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x83), c, _x63), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(f(_x91), false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(a__f(mark(_x91)), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__if(mark(f(false)), c, f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(mark(_x51)), c, f(true)), false, _x33), X3)mark#(if(f(f(_x41)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(false), c, f(true)), false, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(false)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), a__f(mark(_x131)), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(if(_x51, _x52, _x53), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(_x51), mark(_x52), _x53), true, _x33), X3)
mark#(if(if(if(_x41, false, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), false, _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(true, if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x51)), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__f(mark(_x51))), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, c, _x83)), if(_x71, _x72, _x73), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(c, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(c, false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(f(_x61), _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(a__f(mark(_x61)), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(if(c, f(c), _x73)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(if(c, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(true, if(f(c), _x32, _x33), X3)) → a__if#(true, a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, if(_x51, _x52, _x53), _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(f(_x101), _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(a__f(mark(_x101)), mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(X1, if(f(c), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, f(if(_x111, _x112, _x113)), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(a__if(mark(_x111), mark(_x112), _x113)), _x63), _x33), X3)mark#(if(false, if(f(if(if(_x91, _x92, _x93), c, _x73)), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), mark(_x62), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(if(true, if(if(_x71, _x72, _x73), _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(a__if(mark(_x71), mark(_x72), _x73), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x43), X3)
mark#(if(X1, if(f(c), if(c, false, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), a__if(c, false, _x63), _x43), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(f(a__if(mark(false), c, f(true))), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(if(_x71, false, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), false, _x73)), mark(_x32), _x33), X3)mark#(if(f(f(f(if(c, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(c, mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(mark(_x41))), c, f(true)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(f(a__if(mark(mark(_x41)), c, f(true))), a__if(if(c, c, f(true)), c, _x33), X3)
mark#(if(false, if(c, c, _x33), X3)) → a__if#(false, a__if(c, c, _x33), X3)mark#(if(f(if(_x51, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x43), X3)
mark#(if(if(true, if(false, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(false, mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), c, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), c, _x43), X3)
mark#(if(true, if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(true, true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(c, c, f(true)), a__if(if(true, true, _x93), c, _x63), _x43), X3)
mark#(if(X1, if(f(true), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), c, _x33), X3)mark#(if(true, if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(true, a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(if(true, true, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(true, true, _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(c), _x32, _x33), X3)) → a__if#(mark(X1), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, f(_x111), _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), a__f(mark(_x111)), _x83), c, _x63), _x33), X3)
mark#(if(f(f(true)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(true)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)mark#(if(if(true, c, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, c, _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(X1, if(_x31, _x32, _x43), X3)) → a__if#(mark(X1), if(mark(_x31), mark(_x32), _x43), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(true), if(f(c), if(if(f(_x111), true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(a__f(mark(_x111)), true, _x93), c, _x63), _x33), X3)mark#(if(X1, if(f(if(c, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), true, _x43), X3)) → a__if#(f(a__if(mark(false), c, f(true))), if(if(mark(c), c, f(true)), true, _x43), X3)mark#(if(f(if(_x51, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(false, if(f(_x51), _x32, _x43), X3)) → a__if#(false, if(a__f(mark(_x51)), mark(_x32), _x43), X3)mark#(if(f(f(false)), if(f(c), f(_x61), _x33), X3)) → a__if#(a__f(a__f(false)), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(if(true, _x22, _x33), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(if(true, mark(_x22), _x33), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(f(f(f(if(false, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(false, mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(true, if(c, c, _x33), X3)) → a__if#(true, a__if(c, c, _x33), X3)mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x71), mark(_x72), _x73)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(X1, if(f(c), if(c, f(_x101), _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(c, a__f(mark(_x101)), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), a__f(mark(_x71)), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(f(_x71)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__f(mark(_x71))), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), mark(_x62), _x63), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(true), if(f(c), if(c, if(c, false, _x73), _x73), f(true)), X3)) → a__if#(if(mark(true), c, f(true)), if(a__if(c, c, f(true)), if(c, if(c, false, _x73), _x73), _x43), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, false, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x33), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(if(mark(_x21), mark(_x22), _x33), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x41, _x42, _x43)), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x83)), c, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), c, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), false, _x53))), if(if(c, c, f(true)), false, _x43), X3)
mark#(if(f(if(_x51, f(c), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(c), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(a__f(false), a__if(mark(_x71), mark(_x72), _x73), _x53), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(true), if(f(c), if(if(if(_x71, _x72, _x73), true, _x93), c, _x63), _x43), X3)) → a__if#(f(true), if(a__if(mark(c), c, f(true)), a__if(if(a__if(mark(_x71), mark(_x72), _x73), true, _x93), c, _x63), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), true, _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(true), if(f(c), if(if(false, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(false, mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(false), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(if(_x51, f(_x61), _x43)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(if(mark(_x51), a__f(mark(_x61)), _x43)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x63), _x23), if(f(if(c, f(_x91), _x83)), if(true, mark(_x52), _x63), _x33), X3)) → a__if#(a__if(true, if(mark(_x51), mark(_x52), _x63), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(if(true, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(true, mark(_x82), _x93), c, _x63), _x33), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), mark(_x62), _x63), a__if(mark(_x61), mark(_x62), _x63), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(f(a__if(mark(_x61), mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(true, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(true, false, _x103), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x83), c, _x63), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(c, c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x63), _x43), X3)
mark#(if(f(_x21), if(f(c), if(if(true, if(_x111, _x112, _x113), _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, a__if(mark(_x111), mark(_x112), _x113), _x83), c, _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__if(mark(c), c, f(true))), if(if(c, c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(if(true, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(true, mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, c), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, c, _x73), _x33), X3)
mark#(if(f(if(_x51, f(true), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(true), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), f(_x71), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__f(mark(_x71)), _x43), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__if(mark(false), c, f(true)), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(mark(_x51), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__if(mark(false), c, f(true)), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(if(_x21, if(_x51, _x52, _x53), _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(X1, if(f(if(c, f(false), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(false), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(if(_x71, _x72, _x73)), _x32, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(false, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x81, f(_x91), _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(if(c, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(_x21, f(_x51), _x33), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(if(mark(_x21), a__f(mark(_x51)), _x33), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(c, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(c, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(true), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(true, c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)mark#(if(X1, if(f(c), if(_x61, c, _x73), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), if(mark(_x61), c, _x73), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(false, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(if(mark(_x51), mark(_x52), _x43))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(if(false, f(_x51), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(false, a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), f(_x61), _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), a__f(mark(_x61)), _x33), X3)
mark#(if(false, if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(mark(_x61)), c, f(true)), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(false), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(false), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x51, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(_x41, _x42, _x43)), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)
mark#(if(f(false), if(f(c), if(c, if(false, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(false), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(c, if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, true, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)
mark#(if(f(if(_x51, f(if(_x81, if(_x91, _x92, _x93), _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(f(_x91), _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(a__f(mark(_x91)), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(f(if(_x51, f(if(_x81, _x82, _x73)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(if(mark(_x81), mark(_x82), _x73)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(if(_x41, false, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), false, _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), mark(_x62), _x63), a__f(false), _x53)), c, f(true)), if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, mark(_x52), _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), f(c), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__f(c), _x33), X3)mark#(if(X1, if(f(true), true, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(mark(_x51), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(true, if(f(_x71), _x52, _x53), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(a__f(mark(_x71)), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x51, f(f(_x81)), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__f(mark(_x81))), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(f(false)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(false)), a__if(if(mark(c), c, f(true)), false, _x33), X3)
mark#(if(if(true, if(_x51, false, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), false, _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(if(_x91, _x92, _x93), false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(false, mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(X1, if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(if(true, f(false), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(true, a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(false)), if(if(c, c, f(true)), mark(_x32), _x43), X3)mark#(if(if(true, c, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, c, _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(true, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(true, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(true, if(_x51, true, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), true, _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(c)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(c)), if(f(c), if(c, false, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(c, false, _x63), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(false), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(false), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(false, if(f(if(_x81, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, if(_x81, _x82, _x83), _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(a__if(mark(_x81), mark(_x82), _x83)), _x33), X3)
mark#(if(X1, if(f(if(true, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(f(_x51))), if(f(c), c, _x33), X3)) → a__if#(f(f(a__f(mark(_x51)))), a__if(a__if(c, c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(if(_x81, true, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, true, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x43), X3)) → a__if#(a__f(mark(_x21)), if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x43), X3)
mark#(if(f(if(_x51, f(if(_x81, true, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(mark(_x81), true, _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), false, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), false, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(mark(_x71)), mark(_x62), _x63), true, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(_x61, if(_x91, _x92, _x93), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), a__if(mark(_x91), mark(_x92), _x93), _x63), _x33), X3)
mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(mark(_x61)), _x53)), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x43), X3)mark#(if(X1, if(f(if(false, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, c, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(X1, if(f(true), if(_x71, _x72, _x73), _x43), X3)) → a__if#(mark(X1), if(a__f(true), a__if(mark(_x71), mark(_x72), _x73), _x43), X3)mark#(if(f(if(_x51, f(if(_x81, _x82, _x83)), _x43)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(if(mark(_x51), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x43)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(if(if(_x61, _x62, _x63), _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), if(c, if(_x101, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(c), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(mark(_x101), false, _x83), _x73), _x33), X3)mark#(if(f(if(_x51, f(true), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(true), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x63)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(a__if(mark(c), mark(mark(_x82)), _x63), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(if(_x41, if(_x71, _x72, _x73), _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), a__if(mark(_x71), mark(_x72), _x73), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(_x51), c, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), c, _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__if(mark(f(a__if(a__if(a__f(false), false, _x63), mark(_x52), _x53))), c, f(true)), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(f(c)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(_x41)), if(f(c), c, _x33), X3)) → a__if#(a__f(a__if(mark(mark(_x41)), c, f(true))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(X1, if(f(c), if(c, c, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(c, c, _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, f(_x121), _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), a__f(mark(_x121)), _x93), c, _x63), _x33), X3)mark#(if(f(if(_x51, f(if(_x81, _x82, _x73)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(if(mark(_x81), mark(_x82), _x73)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, if(_x91, _x92, _x93), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(X1, if(true, c, _x33), X3)) → a__if#(mark(X1), a__if(true, c, _x33), X3)
mark#(if(false, if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(false, a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(false, if(_x31, true, _x33), X3)) → a__if#(false, a__if(mark(_x31), true, _x33), X3)mark#(if(f(true), if(f(c), if(if(c, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(a__if(mark(c), c, f(true)), a__if(if(c, mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(if(_x51, f(if(false, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(false, mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(c, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(_x41)), if(f(c), false, _x33), X3)) → a__if#(a__f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(X1, if(f(c), if(c, f(_x91), _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(c), c, f(true)), a__if(c, a__f(mark(_x91)), _x63), _x33), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(c, f(c), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(c, false, _x53))), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(a__if(mark(_x71), mark(_x72), _x73), mark(_x62), _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(a__f(false), false, _x53), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(if(_x51, f(_x61), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__if(mark(mark(_x61)), c, f(true)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), false, _x23), if(f(if(true, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(true, false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(if(true, if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(if(c, _x82, _x83)), f(_x61), _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(c, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)mark#(if(f(if(_x51, f(_x61), _x43)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(if(mark(_x51), a__f(mark(_x61)), _x43)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, f(_x91), _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, a__f(mark(_x91)), _x63), _x33), X3)mark#(if(f(f(_x41)), if(f(c), true, _x33), X3)) → a__if#(f(a__f(mark(_x41))), a__if(a__if(mark(c), c, f(true)), true, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(true), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(c, _x72, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(c, mark(_x72), _x73)), mark(_x32), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(if(c, c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(if(if(_x41, true, _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), true, _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__f(false)), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(if(if(_x41, if(_x71, _x72, _x73), _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), a__if(mark(_x71), mark(_x72), _x73), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x53), _x43), X3)) → a__if#(f(true), if(a__if(mark(c), c, f(true)), if(if(mark(_x81), true, _x93), c, _x53), _x43), X3)mark#(if(f(f(c)), if(f(c), if(f(_x81), _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(a__f(mark(_x81)), mark(_x62), _x63), _x33), X3)
mark#(if(if(if(c, _x42, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(c, mark(_x42), _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(c)), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, false, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), false, _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(if(false, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(if(_x101, _x102, _x103)), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(a__if(mark(_x101), mark(_x102), _x103)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(f(a__if(mark(_x71), mark(_x72), _x73)), mark(_x32), _x43), X3)mark#(if(if(true, f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(true)), if(f(c), false, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), false, _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(if(c, c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(a__if(a__if(c, mark(_x62), _x63), mark(_x52), _x53))), if(if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(false, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(false, a__f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(f(_x111)), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(a__f(mark(_x111))), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x51, f(if(if(_x91, _x92, _x93), _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(false)), if(f(c), false, _x43), X3)) → a__if#(a__f(f(false)), if(a__if(mark(c), c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(_x71, f(_x101), _x73)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), a__f(mark(_x101)), _x73)), mark(_x32), _x43), X3)
mark#(if(if(true, _x22, _x23), if(f(if(mark(_x91), f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(f(true), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(true), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(if(if(_x41, _x42, _x53), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(if(mark(_x41), mark(_x42), _x53), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(false, _x22, _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(false, mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), _x22, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__f(false)), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(if(f(_x41), _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(X1, if(f(if(true, _x82, _x83)), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(true, mark(_x82), _x83)), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, true, _x83)), if(true, _x62, _x73), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), true, _x83)), c, f(true)), if(true, mark(_x62), _x73), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), false, _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x53), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), if(true, mark(_x62), _x53), _x43), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(false, mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(X1, if(f(if(c, false, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, false, _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(if(_x51, _x52, _x53))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__if(mark(_x51), mark(_x52), _x53))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(if(mark(_x61), mark(_x62), _x53), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(X1, if(f(if(if(_x91, _x92, _x93), c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(a__if(mark(_x91), mark(_x92), _x93), c, _x73)), c, f(true)), mark(_x32), _x33), X3)mark#(if(X1, if(false, c, _x33), X3)) → a__if#(mark(X1), a__if(false, c, _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(mark(_x51), c, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, c, _x63), _x33), X3)mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(f(_x101)), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), a__f(a__f(mark(_x101))), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(if(if(_x61, _x62, _x63), _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(a__if(mark(_x61), mark(_x62), _x63), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(f(if(_x71, _x72, _x73)), false, _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), mark(_x72), _x73)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(a__if(mark(_x91), mark(_x92), _x93), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(f(_x91), false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__f(mark(_x91)), false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)mark#(if(f(f(c)), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(a__if(a__if(a__f(false), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(_x21, f(true), _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(true), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(true, if(if(_x71, _x72, _x73), _x52, _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(a__if(mark(_x71), mark(_x72), _x73), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(_x61, f(true), _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), a__f(true), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(mark(_x61), a__if(mark(_x71), mark(_x72), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__if(mark(mark(_x71)), c, f(true)), mark(_x62), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), mark(_x102), _x103), _x73), _x53), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(true)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(true)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(c)), if(f(c), if(false, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)
mark#(if(X1, if(f(_x51), false, _x33), X3)) → a__if#(mark(X1), a__if(a__f(mark(_x51)), false, _x33), X3)mark#(if(X1, if(f(true), if(_x61, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(true), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(X1, if(c, true, _x33), X3)) → a__if#(mark(X1), a__if(c, true, _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(c, f(c), _x83)), _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(f(a__f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(_x101, _x102, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x101), mark(_x102), _x103), _x73), _x33), X3)mark#(if(if(true, true, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(true, true, _x23), if(a__if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)
mark#(if(f(_x21), if(f(c), if(c, if(c, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(c, false, _x103), _x73), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(a__f(true), a__if(if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), a__if(a__if(c, c, f(true)), c, _x33), X3)mark#(if(if(if(_x41, _x42, _x43), false, _x33), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(if(a__if(mark(_x41), mark(_x42), _x43), false, _x33), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(c, if(f(if(c, if(_x91, _x92, _x93), _x83)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(a__if(c, a__if(mark(_x91), mark(_x92), _x93), _x83)), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(true, if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), _x23), if(f(if(false, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(f(_x41), f(_x51), _x23), if(f(c), if(mark(_x51), _x62, _x63), _x33), X3)) → a__if#(a__if(a__f(mark(_x41)), a__if(mark(mark(_x51)), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(c, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), if(if(c, c, f(true)), if(c, a__if(c, false, _x103), _x73), _x43), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(if(f(_x61), f(false), _x53)), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(true, false, _x83), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, false, _x83), c, _x63), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, f(_x91)), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__f(mark(_x91)), _x73), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, a__f(c), _x83)), c, f(true)), c, _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, if(f(_x91), false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(a__f(mark(_x91)), false, _x103), _x73), _x33), X3)mark#(if(X1, if(f(if(if(_x101, _x102, _x103), c, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(a__if(mark(_x101), mark(_x102), _x103), c, _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(if(true, _x22, _x23), if(f(if(_x81, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(if(mark(a__if(mark(_x81), a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(true), if(f(c), if(if(_x81, true, _x93), c, _x63), f(true)), X3)) → a__if#(f(true), if(if(c, c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x43), X3)
mark#(if(X1, if(f(false), _x32, _x43), X3)) → a__if#(mark(X1), if(a__f(false), mark(_x32), _x43), X3)mark#(if(if(_x21, f(f(_x81)), _x23), if(f(c), if(mark(f(_x81)), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__if(mark(a__f(mark(_x81))), c, f(true)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), false, _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(c)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__f(c)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), if(true, _x62, _x63), _x33), X3)) → a__if#(a__f(a__f(c)), a__if(if(mark(c), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(if(true, if(_x51, _x52, _x53), _x23), if(f(if(false, f(_x91), _x83)), if(true, true, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), mark(_x52), _x53), _x23), a__if(a__if(mark(a__if(false, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, true, _x63), _x33), X3)
mark#(if(false, if(f(if(_x81, c, _x83)), _x32, _x43), X3)) → a__if#(false, if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), mark(_x32), _x43), X3)mark#(if(X1, if(f(if(c, c, _x73)), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(c, c, _x73)), mark(_x32), _x33), X3)
mark#(if(if(_x21, f(_x51), _x23), if(f(c), if(_x61, true, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), true, _x63), _x33), X3)mark#(if(X1, if(f(if(c, f(c), _x83)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(if(mark(a__if(c, f(c), _x83)), c, f(true)), a__if(mark(mark(_x61)), c, f(true)), _x33), X3)
mark#(if(if(true, f(_x51), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__f(mark(_x51)), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)mark#(if(X1, if(f(if(c, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(c, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), a__if(mark(_x101), c, _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__if(mark(_x61), c, _x63), a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)
mark#(if(if(true, _x22, _x23), if(f(c), if(c, false, _x73), _x33), X3)) → a__if#(a__if(true, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, false, _x73), _x33), X3)mark#(if(if(if(_x41, true, _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), true, _x43), false, _x23), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, c, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__f(c)), a__if(a__if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(c), if(f(c), if(if(true, _x82, _x83), c, _x63), _x33), X3)) → a__if#(a__f(c), a__if(a__if(mark(c), c, f(true)), a__if(a__if(true, mark(_x82), _x83), c, _x63), _x33), X3)mark#(if(f(c), if(f(c), if(c, if(false, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(c), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(_x21), if(f(c), c, _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(f(if(_x51, _x52, _x53)), if(f(c), if(c, true, _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), mark(_x52), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, true, _x73), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(true, a__if(mark(_x101), mark(_x102), _x103), _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(if(_x21, _x22, _x23), if(_x31, _x32, _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(mark(_x31), mark(_x32), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x43), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x43), X3)mark#(if(X1, if(_x31, f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(mark(_x31), a__f(mark(_x61)), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), mark(_x72), _x73), _x63), a__f(mark(_x61)), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), a__if(mark(_x71), c, _x73), _x63), mark(_x52), _x53))), if(a__if(c, c, f(true)), false, _x43), X3)
mark#(if(f(f(false)), if(f(c), c, _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), c, _x33), X3)mark#(if(false, if(f(_x51), _x32, _x33), X3)) → a__if#(false, a__if(a__if(mark(mark(_x51)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), _x32, _x43), X3)) → a__if#(a__f(f(mark(_x41))), if(a__if(mark(c), c, f(true)), mark(_x32), _x43), X3)mark#(if(if(if(false, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(false, mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(f(if(c, f(f(_x81)), _x53)), if(f(c), if(c, if(false, false, _x83), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(c, a__f(a__f(mark(_x81))), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, if(false, false, _x83), _x73), _x33), X3)mark#(if(f(f(_x41)), if(f(c), _x32, _x33), X3)) → a__if#(f(a__if(mark(mark(_x41)), c, f(true))), a__if(if(c, c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(true, a__f(false), _x53)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(f(false)), if(f(c), _x32, _x43), X3)) → a__if#(f(f(false)), if(if(mark(c), c, f(true)), mark(_x32), _x43), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, f(true)), X3)) → a__if#(a__f(f(true)), if(if(c, c, f(true)), false, _x43), X3)mark#(if(if(if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x43), false, _x23), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x43), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), false, _x23), if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x43), X3)
mark#(if(f(if(_x41, _x42, _x43)), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__f(a__if(mark(_x41), mark(_x42), _x43)), a__if(a__if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(c, if(_x101, false, _x103), _x73), f(true)), X3)) → a__if#(if(mark(mark(_x21)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(X1, if(f(c), if(_x61, _x62, _x63), _x43), X3)) → a__if#(mark(X1), if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x43), X3)mark#(if(f(if(_x51, false, _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), false, _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(f(c)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(c), c, f(true))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(if(_x21, f(false), _x23), if(f(c), if(_x61, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(false), _x23), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), mark(_x62), _x63), _x33), X3)
mark#(if(f(f(f(if(_x61, true, _x63)))), if(f(c), c, _x33), X3)) → a__if#(a__f(f(a__f(a__if(mark(_x61), true, _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)mark#(if(X1, if(f(c), if(c, _x62, _x63), _x33), X3)) → a__if#(mark(X1), a__if(a__if(c, c, f(true)), a__if(c, mark(_x62), _x63), _x33), X3)
mark#(if(if(true, if(_x51, if(_x81, _x82, _x83), _x53), _x23), if(f(if(c, f(_x91), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(true, a__if(mark(_x51), a__if(mark(_x81), mark(_x82), _x83), _x53), _x23), a__if(a__if(mark(a__if(c, a__f(mark(_x91)), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(f(false)), if(f(c), f(if(_x81, _x82, _x83)), _x33), X3)) → a__if#(a__f(f(false)), a__if(if(mark(c), c, f(true)), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, false, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, false, _x63), _x33), X3)mark#(if(X1, if(f(if(false, _x82, _x83)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(a__if(false, mark(_x82), _x83)), c, f(true)), mark(_x32), _x43), X3)
mark#(if(if(if(_x41, _x42, _x43), false, _x33), if(f(if(_x81, false, _x83)), if(true, _x62, _x71), _x33), X3)) → a__if#(if(a__if(mark(_x41), mark(_x42), _x43), false, _x33), a__if(a__if(mark(a__if(mark(_x81), false, _x83)), c, f(true)), mark(mark(_x62)), _x33), X3)mark#(if(c, if(f(if(c, false, _x73)), _x32, _x33), X3)) → a__if#(c, a__if(a__if(mark(if(c, false, _x73)), c, f(true)), mark(_x32), _x33), X3)
mark#(if(f(f(false)), if(f(c), _x32, _x33), X3)) → a__if#(a__f(a__if(mark(false), c, f(true))), a__if(if(mark(c), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(f(f(c)), if(a__if(mark(c), c, f(true)), false, _x43), X3)
mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x33), X3)) → a__if#(a__if(mark(if(a__f(c), a__f(false), _x43)), c, f(true)), a__if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, true, _x93), c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), true, _x93), c, _x63), _x33), X3)
mark#(if(X1, if(f(false), _x32, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(false), c, f(true)), mark(_x32), _x33), X3)mark#(if(f(false), if(f(c), if(c, if(_x101, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(false), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x33), X3)
mark#(if(f(false), if(f(c), if(_x61, c, _x63), _x33), X3)) → a__if#(a__f(false), a__if(a__if(mark(c), c, f(true)), a__if(mark(_x61), c, _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(c), if(if(_x81, _x82, _x83), _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(c), c, f(true)), a__if(a__if(mark(_x81), mark(_x82), _x83), mark(_x62), _x63), _x33), X3)
mark#(if(f(c), if(f(c), if(c, if(_x101, false, _x103), _x73), _x43), X3)) → a__if#(a__if(mark(c), c, f(true)), if(a__if(mark(c), c, f(true)), if(c, a__if(mark(_x101), false, _x103), _x73), _x43), X3)mark#(if(if(_x21, f(_x51), _x23), if(f(if(_x81, f(true), _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), a__f(mark(_x51)), _x23), a__if(a__if(mark(a__if(mark(_x81), a__f(true), _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)
mark#(if(if(if(_x41, _x42, _x43), _x22, _x23), if(f(if(_x81, c, _x83)), if(true, _x62, _x63), _x33), X3)) → a__if#(a__if(a__if(mark(_x41), mark(_x42), _x43), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), c, _x83)), c, f(true)), a__if(true, mark(_x62), _x63), _x33), X3)mark#(if(f(_x21), if(f(c), if(if(_x81, _x82, _x93), c, _x63), _x33), X3)) → a__if#(f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(if(mark(_x81), mark(_x82), _x93), c, _x63), _x33), X3)
mark#(if(true, if(f(c), if(false, _x62, _x63), _x33), X3)) → a__if#(true, a__if(a__if(mark(c), c, f(true)), a__if(false, mark(_x62), _x63), _x33), X3)mark#(if(if(_x21, _x22, _x23), if(f(if(_x81, _x82, _x83)), if(true, c, _x63), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__if(mark(a__if(mark(_x81), mark(_x82), _x83)), c, f(true)), a__if(true, c, _x63), _x33), X3)
mark#(if(f(_x21), if(f(c), if(c, c, _x63), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__if(mark(c), c, f(true)), a__if(c, c, _x63), _x33), X3)mark#(if(f(if(mark(c), f(false), f(true))), if(f(c), if(c, if(false, false, _x81), _x73), _x43), X3)) → a__if#(a__if(mark(a__if(mark(_x51), a__f(false), _x53)), c, f(true)), if(if(mark(c), c, f(true)), if(c, mark(_x81), _x73), _x43), X3)
mark#(if(X1, if(f(if(c, f(c), _x83)), c, _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(c, f(c), _x83)), c, f(true)), c, _x33), X3)mark#(if(if(false, _x22, _x23), if(f(c), if(c, _x62, _x73), _x33), X3)) → a__if#(a__if(false, mark(_x22), _x23), a__if(if(mark(c), c, f(true)), if(c, mark(_x62), _x73), _x33), X3)
mark#(if(X1, if(f(if(_x81, c, _x93)), _x32, _x43), X3)) → a__if#(mark(X1), if(a__if(mark(if(mark(_x81), c, _x93)), c, f(true)), mark(_x32), _x43), X3)mark#(if(f(f(f(if(_x61, _x62, _x63)))), if(f(c), c, _x33), X3)) → a__if#(f(f(a__f(a__if(mark(_x61), mark(_x62), _x63)))), a__if(a__if(mark(c), c, f(true)), c, _x33), X3)
mark#(if(f(f(a__if(mark(c), c, f(true)))), if(f(c), false, _x43), X3)) → a__if#(a__f(f(a__if(a__if(a__f(false), false, _x63), false, _x53))), if(a__if(c, c, f(true)), false, _x43), X3)mark#(if(f(if(f(_x61), f(false), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(a__f(mark(_x61)), a__f(false), _x53)), c, f(true)), a__if(a__if(mark(c), c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)
mark#(if(f(if(_x51, f(if(_x81, _x82, _x83)), _x53)), if(f(c), if(c, if(false, false, _x103), _x73), _x33), X3)) → a__if#(a__if(mark(a__if(mark(_x51), f(a__if(mark(_x81), mark(_x82), _x83)), _x53)), c, f(true)), a__if(a__if(c, c, f(true)), if(c, a__if(false, false, _x103), _x73), _x33), X3)

Rewrite Rules

a__f(X) → a__if(mark(X), c, f(true))a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)mark(c) → c
mark(true) → truemark(false) → false
a__f(X) → f(X)a__if(X1, X2, X3) → if(X1, X2, X3)

Original Signature

Termination of terms over the following signature is verified: f, a__if, c, if, true, false, mark, a__f

Strategy

The right-hand side of the rule mark#(if(X1, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a__if#(mark(X1), a__if(a__f(a__if(false, c, _x73)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__f(a__if(c, c, _x73)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(a__f(mark(_x81))), _x33), X3) 
a__if#(mark(X1), a__if(f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3) 
a__if#(true, a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__f(a__if(true, c, _x73)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__f(a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x73)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(c), _x33), X3) 
a__if#(a__f(mark(_x21)), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__f(a__if(a__f(mark(_x81)), c, _x73)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(false), _x33), X3) 
a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__if(mark(mark(_x61)), c, f(true)), _x33), X3) 
a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x33), X3) 
a__if#(mark(X1), if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x43), X3) 
a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), f(mark(_x61)), _x33), X3) 
a__if#(c, a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3) 
a__if#(false, a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__f(if(mark(_x71), c, _x63)), a__f(mark(_x61)), _x33), X3) 
a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(true), _x33), X3) 
Thus, the rule mark#(if(X1, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3) is replaced by the following rules:
mark#(if(X1, if(f(if(true, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(true, c, _x73)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(false, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(false, c, _x73)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(mark(_x61), c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__if(mark(mark(_x61)), c, f(true)), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), f(if(_x81, _x82, _x83)), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(a__if(mark(_x81), mark(_x82), _x83)), _x33), X3)
mark#(if(X1, if(f(if(f(_x81), c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__f(mark(_x81)), c, _x73)), a__f(mark(_x61)), _x33), X3)mark#(if(c, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(c, a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3)
mark#(if(true, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(true, a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x63)), f(mark(_x71)), _x33), X3)) → a__if#(mark(X1), a__if(a__f(if(mark(_x71), c, _x63)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), f(f(_x81)), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(a__f(mark(_x81))), _x33), X3)mark#(if(f(_x21), if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(a__f(mark(_x21)), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), f(true), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(true), _x33), X3)mark#(if(X1, if(f(if(if(_x81, _x82, _x83), c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(a__if(mark(_x81), mark(_x82), _x83), c, _x73)), a__f(mark(_x61)), _x33), X3)
mark#(if(X1, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__if(mark(a__if(mark(_x71), c, _x73)), c, f(true)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), f(_x61), _x43), X3)) → a__if#(mark(X1), if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x43), X3)
mark#(if(X1, if(f(if(mark(_x61), c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), f(false), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(false), _x33), X3)
mark#(if(X1, if(f(if(c, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(c, c, _x73)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(mark(X1), a__if(f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3)
mark#(if(false, if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(false, a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3)mark#(if(X1, if(f(if(_x71, c, _x73)), f(c), _x33), X3)) → a__if#(mark(X1), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(c), _x33), X3)
mark#(if(if(_x21, _x22, _x23), if(f(if(_x71, c, _x73)), f(_x61), _x33), X3)) → a__if#(a__if(mark(_x21), mark(_x22), _x23), a__if(a__f(a__if(mark(_x71), c, _x73)), a__f(mark(_x61)), _x33), X3)